Post on 03-Jan-2016
Accelerated Math Geometry Unit
Objective students will be able to understand the basics concepts of geometry and be able to
apply them to real world problems
AnglesTrianglesCircles3-D ShapesAreaVolumeSurface Area
Topics we will coverhellip
Letrsquos Get Started
Angle and line relationships
Objective to be able to examine relationships between pairs of angles examine
relationships of angles formed by parallel lines and a transversal
Key concept pairs of angles
Vertical Angles
When two lines intersect they form two pairs of opposite angles
Angles are congruent
Model
41
23
1 23 4
ampamp
Symbol
1 2
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
AnglesTrianglesCircles3-D ShapesAreaVolumeSurface Area
Topics we will coverhellip
Letrsquos Get Started
Angle and line relationships
Objective to be able to examine relationships between pairs of angles examine
relationships of angles formed by parallel lines and a transversal
Key concept pairs of angles
Vertical Angles
When two lines intersect they form two pairs of opposite angles
Angles are congruent
Model
41
23
1 23 4
ampamp
Symbol
1 2
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Letrsquos Get Started
Angle and line relationships
Objective to be able to examine relationships between pairs of angles examine
relationships of angles formed by parallel lines and a transversal
Key concept pairs of angles
Vertical Angles
When two lines intersect they form two pairs of opposite angles
Angles are congruent
Model
41
23
1 23 4
ampamp
Symbol
1 2
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Angle and line relationships
Objective to be able to examine relationships between pairs of angles examine
relationships of angles formed by parallel lines and a transversal
Key concept pairs of angles
Vertical Angles
When two lines intersect they form two pairs of opposite angles
Angles are congruent
Model
41
23
1 23 4
ampamp
Symbol
1 2
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Key concept pairs of angles
Vertical Angles
When two lines intersect they form two pairs of opposite angles
Angles are congruent
Model
41
23
1 23 4
ampamp
Symbol
1 2
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Key concept pairs of angles
Adjacent Angles
When two angles have the same vertex between them share a common side and do not overlap
Model
41
23
1 33 2
ampamp
Symbol
1 3ampare adjacent angles
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Key concept pairs of angles
Complementary Angles
When two angles have the sum of 90o
Model
35o
65o
Symbol
35o + 65o = 90o
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Key concept pairs of angles
Supplementary Angles
When two angles have the sum of 180o
Model
35o
145o
Symbol
35o + 145o = 180o
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Key concept pairs of angles
Perpendicular Lines
When two lines intersect to form a right angle
Model
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Example 1
Jan is cutting a corner off a piece of rectangular tile Classify the
relationship between angle x and angle y
If the m y = 135o what is the measure of x
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Special Angle RelationshipsThe following pairs of angles are congruent Alternate Interior Angles are
on opposite sides of the transversal and inside the parallel lines Angles 3 amp 5 Angles 4 amp 6
Alternate Exterior Angles are on opposite sides of the transversal and outside the parallel lines Angles 1 amp 7 Angles 2 amp 8
Corresponding Angles are in same position on the parallel lines in relation to the transversal Angles 1 amp 5 Angles 2 amp 6
214
758
6
3
Parallel Line
Parallel Line
Transversal Line (a line that intersects two parallel lines
When a transversal intersects it forms 8 angles Interior and exterior angles
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Example 2 (page 496 in book)
Using the figure from page 496 answer the following questionsa) Classify the relationship between angle 3 and angle 5
Since angle 3 and angle 5 are alternate interior
angles they are congruent
b) If the measure of angle 1 is 120 degrees the find the measure of angle 5 and angle 3
Since angle 1 and angle 5 are corresponding angles they are
congruent and angle 5 measures 120 degrees
Since angle 5 and angle 3 are congruent angle 3 measures
120 degrees also
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Example 3 (page 496 in book)Using the figure in the book answer the following questions
Measure of angle ABD = 164o
Find the measures of angle ABC and CBD
(2x + 23)o Xo
A
C
D
B
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Letrsquos Do Some Guided Practice
Open Your Books
Way to Go
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying
Triangles
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
All Triangles Have 3 Names
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
First MiddleLast
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Letrsquos look at the first nameshellip
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
First Names
ACUTE
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Acute
3 acute angles that measure less than 90o
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
First Names
OBTUSE
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Obtuse
1 obtuse angle that measures greater than 90o
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
First Names
RIGHT
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Right
1 right angle that measures 90o
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Letrsquos look at the middle nameshellip
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Middle Names
SCALENE
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Scalene
No equal sides
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Middle Names
ISOSCELES
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Isosceles
2 equal sides
Shows that the sides are of equal length
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Middle Names
EQUILATERAL
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Equilateral
3 equal sides
Shows that the sides are of equal length
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Letrsquos look at the last namehellip
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Last Name
TRIANGLE
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Letrsquos look at some exampleshellip
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Obtuse Scalene Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Acute Isosceles Triangle
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
What is the full name of this triangle
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Acute Equilateral
Triangle
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Looking Good letrsquos playhellip
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Awesome Job
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
NAME THAT TRIANGLE
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Here are some simple rules Everyone will be in teams chosen by the teacher
Everyone will have a turn at writing the answer
Each player will write the answer of their choosing WITHOUT the help from their teammates That means NO TALKING DURING EACH ROUND
Negative comments will result in loss of points
Talking DURING rounds will result in loss of points
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
LETrsquoS PLAY
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
AcuteEquilateral
Triangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
ObtuseIsoscelesTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
ObtuseScaleneTriangle
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
20191817161514131211
10987654321
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Name That Triangle
RightScaleneTriangle
Name That Triangle
GREAT JOB EVERYONE
Do we need a tie breaker
Classifying Triangles
Letrsquos find the measures of
triangles
Classifying Triangles
All triangles measure
180o
Classifying Triangles
What do they measure
180o
Classifying Triangles
71o
64o
X
Letrsquos find x
Classifying Triangles
71o
64o
X
64o + 71o = 135o
180o - 135o = 45o
x = 45o
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
All triangles measure
180o
Classifying Triangles
What do they measure
180o
Classifying Triangles
71o
64o
X
Letrsquos find x
Classifying Triangles
71o
64o
X
64o + 71o = 135o
180o - 135o = 45o
x = 45o
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
What do they measure
180o
Classifying Triangles
71o
64o
X
Letrsquos find x
Classifying Triangles
71o
64o
X
64o + 71o = 135o
180o - 135o = 45o
x = 45o
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
71o
64o
X
Letrsquos find x
Classifying Triangles
71o
64o
X
64o + 71o = 135o
180o - 135o = 45o
x = 45o
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
71o
64o
X
64o + 71o = 135o
180o - 135o = 45o
x = 45o
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
38o
Letrsquos find x
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
38o
90o + 38o = 128o
180o - 128o = 52o
x = 52o
X
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
Now find the measures of the
triangles
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
40o
Letrsquos find x
X
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
40o
X = 50o
X
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
40o
Letrsquos find x
X 25o
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
40o
X = 115o
X 25o
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
60o
Letrsquos find x
X60o
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
60o
X = 60o
X60o
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Classifying Triangles
Letrsquos put our new information to the test and start our
assignment for the day
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circle Time
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Parts of a Circle
RadiusDiameterCentral AngleChordSemi Circle
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Radius
What is it A segment that
connects the center point of a circle to the circumference of the circle
A
B
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Radius
How do you name it You name a radius like
a line segment starting with the center point first
Example ABA
B
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Diameter
What is it A segment that
passes the center of a circle and has both endpoints on the circumference of the circle
BC A
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Diameter
How do you name it You name a diameter
just like a line segment do not name the center point
Example CB or BC B
C A
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Chord
What is it A segment that has
both endpoints on the circumference of the circle
C
B
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Chord
How do you name it You name a chord just
like you would a line segment
Example BC or CB
C
B
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Objective to be able to use the formulas for circumference and area to solve real world
problems
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
What is Pi
prodIntro to Pi Video
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Pi
prod = 314159hellip
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Pi
Pi is an irrational numberMeaning it goes on forever and never repeats
So far mathematicians have discovered over 134 million digits of pi
Theyrsquore still working to find morehellip
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Pi
But all you need to know ishellip
prod = 314
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Pi
Pi is a ratio of circumference (C) to diameter (d)
Cd = prod
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
Circumference is the distance around a circle
Circumference is measured in units
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
C = (d) prodor
C =(2) (r) prod
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
Find the circumferencehellip
C = 10 bull 314
C = 314 m
10 m
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
Find the circumferencehellip
C = 2 bull 2 bull 314
C = 1256 in
2 in
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
Find the circumferencehellip
C = 2 bull 8 bull 314
C = 5024 yd
8 yd
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference
Find the circumferencehellip
C = 2 bull 314
C = 628 cm
2 cm
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Great Now letrsquos move on to area
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Area is the number of square units that fit inside a circle
Area is measured in units2
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
A = prod r2
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Can also be writtenhellip
A = prod bull r bull r
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Find the areahellip
A = 314 bull 6 bull 6
A = 11304 km2
6 km
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Find the areahellip
A = 314 bull 4 bull 4
A = 5024 mi2
8 mi
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Find the areahellip
A = 314 bull 15 bull 15
A = 7065 m2
15 m
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Area
Find the areahellip
A = 314 bull 35 bull 35
A = 38465 ft2
7 ft
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Super work
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
So how does this apply in
the real world
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Social Studies The circular base of the teepees of the Sioux and
Cheyenne tribes have a diameter of about 15 ft What is the area of the base to the nearest square unit
r = 15 divide 2 r = 75 ft A = 314 bull 75 bull 75 A = 176625
A asymp 177 ft2
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Technology Airport Surveillance Radar (ASR) tracks planes in
a circular region around an airport What is the area covered by the radar if the diameter of the circular region is 120 nautical miles
r = 120 divide 2 r = 60 nautical miles A = 314 bull 60 bull 60
A = 11304 square nautical mi
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Archaeology The large stones of Stonehenge are arranged in a
circle about 30 m in diameter How many meters would you have to walk if you wanted to walk the entire distance around the structure
d = 30 m C = 30 bull 314
C = 942 m
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circumference amp Area
Way to go
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Objective to be able to find area of composite figures and use that process to solve real life
problems
Area of Composite Figures
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
SquareRectangle
L bull W
Letrsquos review formulas for area
4 ft
7 ft
9 cm
28 ft2
81 cm2
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Triangle
frac12 b bull h
Letrsquos review formulas for area
5 ft
4 ft
10 ft2
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Circle
314 bull r2
Letrsquos review formulas for area
11304 in2
6 in
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Practice
43 m
92 m
1978 m2
725 m
3 m
2175 m2
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Practice
19625 m2
15 m
225 m2
5 cm
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Way to go
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos look at some new formulas for area
Parallelogram
b bull h 5 ft
7 ft
4 ft
35 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos practice the new formula for area
Parallelogram
b bull h 6 ft
12 ft
4 ft
72 ft2
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos practice the new formula for area
Parallelogram
b bull h 25 in
8 in
35 in
280 in2
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
TrapezoidJust a reminderhellipname the only characteristic that trapezoids have
1 set of parallel sides
Letrsquos look at another new formula for area
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Trapezoid
frac12 h(b1 + b2)
Letrsquos look at another new formula for area
4 in
7 in
2 in
11 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
10 in
4 in
6 in
32 in2
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Trapezoid
frac12 h(b1 + b2)
Letrsquos practice the new formula for area
23 in
17 in
9 in
180 in2
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos practice
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos look at composite figures now
Composite Figures are made up of two or more shapes
To find the area of a composite figure you must decompose the figure into shapes with areas that you know and then find the sum of these areas
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Find the area of the composite figureThe area can be
separated into a semicircle and a triangle
frac12 (314)(r2) for circle
frac12 (b)(h) for triangle
Example 1
6 m
11 m
141 m 33 m+ 471 m2=
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Find the area of the composite figure The area can be
separated into a trapezoid and a rectangle
frac12 h (b1 + b2) for trapezoid
L bull W for square
Example 1
20 m
825 m 400 m+ 4825 m2=
20 m
25 m
13 m
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Awesome Work
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Pedrorsquos father is building a shed How many square feet of wood is needed to build the back of the shed shown at the right
Letrsquos try word problems
15 ft
12 ft
4 ft
210 ft2
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Find the area of each shape and subtract
What about shaded areas
4 cm
3 cm
13 cm
7 cm
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos practice
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume of Prisms
Objective to be able to find the volume of certain 3-D shapes to solve real world
problems
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
VolumeVolume of a three-dimensional figure is the
number of cubic units needed to fill the space inside the figure
A cubic unit is a cube with edges 1 unit long
1 cm1 cm
1 cm
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume To solve for volumehellip
area of the base bull the height
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume Measured in cubic feethellip
cm3
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Rectangular Solids
length bull width bull height
LW
H
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try It
12 bull 6 bull 8 =
Rectangular Solids
576 cm3
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try Some on Your
Own
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Triangular Prisms
frac12 bull base bull height bull width
H
B
W
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try It
frac12 bull 8 bull 10 bull 60 =2400 cm3
Triangular Prisms
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try Some on Your
Own
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Cylinders
314 bull radius bull radius bullheight
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try It
314 bull 5 bull 5 bull 14 =
Cylinders
14
5
1099 cm3
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Letrsquos Try Some Word Problems
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume
A semi has a trailer that is 32 inches long 12 inches wide and 22 inches high What is the volume of the
trailer
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume
A tent has the shape of a triangular prism From the
floor to the peal is 9 feet The floor is 22 feet wide and 35
feet long What is the volume of the tent
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
Volume
A bucket has a diameter of 20 centimeters and a
height of 15 centimeters What is the volume
You are sooo good
Rectangular Solids
You are sooo good
Rectangular Solids