Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in...
-
Upload
daniel-robertson -
Category
Documents
-
view
218 -
download
1
Transcript of Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in...
![Page 1: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/1.jpg)
Module 5 Test Review
![Page 2: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/2.jpg)
Now is a chance to review all of the great stuff you have been learning in Module 5!
– Area of Triangles– Area of Quadrilaterals– Area of Polygons– Shapes on the Coordinate Plane– Surface Area of Prisms– Surface Area of Pyramids
![Page 3: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/3.jpg)
Area
Area:
The amount of square units contained within a plane, or a two-dimensional figure.
![Page 4: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/4.jpg)
Area of a Rectangle - Review
Count each square unit within the rectangle. There are 21 square units. This method works if you have the shape on a grid.
Area can be found with or without a coordinate plane by multiplying the length by the width.7 × 3 = 21 square units.Therefore, the area of this rectangle is 21 units squared.
![Page 5: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/5.jpg)
Area of a Triangle
![Page 6: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/6.jpg)
![Page 7: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/7.jpg)
![Page 8: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/8.jpg)
Perpendicular Lines
"Perpendicular" means two lines that intersect to form a right angle (90 degrees).
![Page 9: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/9.jpg)
Area of an Acute Triangle
![Page 10: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/10.jpg)
Area of an Right Triangle
![Page 11: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/11.jpg)
Total Area
• Using the same triangles from our earlier examples, use this example to see how you can find total area
The area of the acute triangle was 24 square inches. The area of the right triangle was 12 square inches.
Area of all three triangles = 24 + 12 + 12 = 48 square inches.
The area of the rectangle = 8 inches × 6 inches = 48 square inches.
![Page 12: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/12.jpg)
QuadrilateralsA parallelogram is a four-sided polygon with two pairs of parallel and congruent sides.
You can identify which sides are congruent because you will see matching tick marks on them.
The rhombus is a parallelogram where all the sides are congruent.
A square is a special rhombus where all sides are congruent and perpendicular.
A kite has two pairs of congruent sides.
The important thing about the congruent sides is that they are adjacent (or next) to each other, not on opposite sides from each other.
A trapezoid is a quadrilateral in which one pair of opposite sides is parallel.You can see which sides are parallel because of the arrowhead.These sides are called bases of the trapezoid. The other sides can be of any length.
![Page 13: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/13.jpg)
Area of Parallelogram
A parallelogram can be decomposed into two right triangles with a rectangle in between them. Drawing vertical lines from the corners to the base will create a height for the side triangles and a width for the rectangle. The important thing to notice is that the two side triangles are congruent.
![Page 14: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/14.jpg)
Area of Parallelogram
To calculate the area of the parallelogram, add up the area of each shape created from the decomposition.
![Page 15: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/15.jpg)
Area of a Rhombus
One way to compose a rhombus is by putting two congruent triangles together, so its decomposition would be just that.
![Page 16: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/16.jpg)
Area of a Rhombus
Triangle A: The base is 8 inches, and the height is 4 inches.
A = bh
A =
A =
A = 16 in2
Triangle B:It will have the same area since it is congruent.
Area = triangle A + Triangle BA = 16 + 16A = 32 in2
![Page 17: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/17.jpg)
Area of a Kite
A kite is composed of 4 right triangles.
Triangle A and B are congruent
Triangle C and D are congruent So to find the area of the kite, you need to just find the area of Triangle A and C, then double it.
![Page 18: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/18.jpg)
Area of a Kite
Triangle A:The base is 6 ft., and the height is 7 ft.
Triangle C:The base is 16 ft., and the height is 7 ft.
Remember, triangle A and B are congruent, and triangle C and D are congruent.
Total Area = 2A + 2CA = 2(21) + 2(56)A = 42 + 112A = 154 ft2
![Page 19: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/19.jpg)
Area of a Right Trapezoid
• How can you decompose this Right Trapezoid?
![Page 20: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/20.jpg)
Area of a Right Trapezoid
Triangle: The base is 2 m, and the height is 6.5 m.
Rectangle: The length is 6.5 m, and the width is 5 m.
Total area = Triangle + rectangleA = 6.5 + 32.5A = 39 m2
![Page 21: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/21.jpg)
Area of an Acute Trapezoid
• Can you use the decomposition method to find the area of this trapezoid?
![Page 22: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/22.jpg)
Check your work
![Page 23: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/23.jpg)
Polygons
Polygons can be classified as regular or irregular.
Regular polygon:A polygon that has all congruent sides and angles.
Irregular polygon:A polygon that does not have all congruent sides and angles
![Page 24: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/24.jpg)
Examples of Polygons
![Page 25: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/25.jpg)
Regular Polygons
How can we decompose this hexagon to find the area?
The key to decomposing and composing polygons is to use only shapes you are familiar with. You would not want to decompose this hexagon into a shape you do not have the dimensions for or that you do not know how to solve for the area of.
![Page 26: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/26.jpg)
Regular Polygons
Method 2
![Page 27: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/27.jpg)
Irregular Polygons
• Keep in mind there may be more than one way you can decompose an irregular polygon
• Here are two examples of how we can deconstruct this irregular polygon
![Page 28: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/28.jpg)
Irregular Polygons
To calculate the area of this irregular polygon, all you need to do is calculate the area of each rectangle, then calculate the sum of the areas. Recall, the area of a rectangle A = l x w
Area of smaller rectangle 5 cm × 3 cm = 15 cm2
Area of larger rectangle 10 cm × 6 cm = 60 cm2
Total area of irregular polygon 15 cm2 + 60 cm2 = 75 cm2
![Page 29: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/29.jpg)
Using a net to find Surface Area
• We can use the net of the rectangular prism to find the surface area.
• Drawing your net is the first step.
![Page 30: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/30.jpg)
Using Nets to find the Surface Area
Next you want to find the area of each part:
To find the total area or Surface area, you add up the areas of the partsSA = 110 + 22 + 110 + 22 + 110 + 20 + 20 = 304 in2
![Page 31: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/31.jpg)
Try It!
Use a net to solve for the surface area
![Page 32: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/32.jpg)
Check your work
![Page 33: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/33.jpg)
Surface of Triangular Prisms
Nico wants to stain his new skateboard ramp shown in the image with varnish
What is the total surface area of the prism?
![Page 34: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/34.jpg)
Surface Area of a Triangular Prism
First, draw your net.
Now we need to find the area of each part.
![Page 35: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/35.jpg)
Surface area of Triangular Prisms
![Page 36: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/36.jpg)
Surface Area of Pyramids
We can use the nets of Pyramids to find the surface area.
Now, let's calculate the area of the square base. Area of the square base:8 in × 8 in = 64 in2
The last part in the calculation is to just determine the sum of all the faces. Total surface area of the pyramid:176 in2 + 64 in2 = 240 in2
![Page 37: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/37.jpg)
Try it
Can you find the surface area of this pyramid?
![Page 38: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/38.jpg)
Check your work
Total surface area:130 cm2 + 163.48 cm2 + 134 cm2 = 427.48 cm2
![Page 39: Module 5 Test Review. Now is a chance to review all of the great stuff you have been learning in Module 5! –Area of Triangles –Area of Quadrilaterals.](https://reader035.fdocuments.net/reader035/viewer/2022062517/56649ef35503460f94c062de/html5/thumbnails/39.jpg)
You have now had a chance to review all of the great stuff you learned in Module 5!
• Area of Triangles• Area of Quadrilaterals• Area of Polygons• Shapes on the Coordinate Plane• Surface Area of Prisms• Surface Area of Pyramids
Have you completed all assessments in module 5? Have you completed your Module 5 DBA?
Now you are ready to move forward and complete your module 5 test. Please make sure you are ready to complete your test before you enter the test session.