Geometry Unit 10 & 11 Note Sheets
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Date Name of Lesson
10.1 Areas of Parallelograms, Triangles
10.2 Areas of Trapezoids, Rhombi and Kites
10.3 Area of Circles and Sectors
10.4 Areas of Regular Polygons and Composite Figures
10.5 Area of Nonrigid Transformations
10.6 Surface Area
11.1 Cross Section and Solids of Revolution
11.2 Volume of Prisms and Cylinders
11.3 Volume of Pyramids and Cones
11.4 Volume of Spheres
11.6 Volume of Nonrigid transformations
11.7 Applying Measurements
Geometry Unit 10 & 11 Note Sheets
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Area of Figures Review
Circle Sector of a Circle Parallelogram Triangle Trapezoid Rhombi and Kites
r – radius
d -diameter
r – radius
x – degree of
sector
A-area of sector
𝐴 = 𝜋𝑟2
𝐶 = 2𝜋𝑟
𝐶 = 𝑑𝜋
Proportion: 𝐴
𝜋𝑟2=
𝑥
360°
Equation:
𝐴 =𝑥
360°𝜋𝑟2
𝐴 = 𝑏ℎ
𝐴 =1
2𝑏ℎ
𝐴1
2(𝑏1 + 𝑏2)ℎ
𝑑1, 𝑑2: 𝐷𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠
𝐴 =1
2𝑑1𝑑2
Geometry Unit 10 & 11 Note Sheets
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Surface Area of Figures Prism Cylinder Pyramid Cone
P: perimeter of the base
B: area of the base
h: height of prism
𝑆 = 2𝐵 + 𝑃ℎ
r: radius
h: height of cylinder
𝑆 = 2𝜋𝑟2 + 2𝜋𝑟ℎ
P: perimeter of the base
B: area of the base
l: slant height
𝑆 =1
2𝑃𝑙 + 𝐵
r: radius
l: slant height
𝑆 = 𝜋𝑟2+𝜋𝑟𝑙
Geometry Unit 10 & 11 Note Sheets
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10.1 Areas of Parallelograms, Triangles and Notes
Review – Define Parallelogram ________________________________________________________________
Area of a Parallelogram
Guided Practice
Find the perimeter and the area of the figure.
1. 2.
Your Turn
3. 4.
Area of a Triangle
Guided Practice
Find the perimeter and area of the figure.
5. 6.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
7. 8.
Guided Practice Your Turn
Find x.
9. 10.
Guided Practice
11. Find the perimeter and area of △ABC with vertices A(4, –2), B(12, 6), and C(–4, 6).
Your turn
12. Find the perimeter and area of △ABC with vertices A(1, 3), B(1, -1), and C(5, -1).
Geometry Unit 10 & 11 Note Sheets
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10.2 Areas of Trapezoids, Rhombi, and Kites Notes
Area of a Trapezoid
Guided Practice
Find the area of the figure.
1.
Your Turn
2.
Area of a Rhombus or Kite
Geometry Unit 10 & 11 Note Sheets
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Guided Practice
Find the area of the figure.
3. 4.
Your Turn
5. 6.
Guided Practice
7. One diagonal of a rhombus is half as long as the other diagonal. If the area of the rhombus is 64 square
inches, what are the lengths of the diagonals?
Your Turn
8. One diagonal of a kite is twice as long as the other diagonal. If the area of the kite is 240 square inches,
what are the lengths of the diagonals?
Geometry Unit 10 & 11 Note Sheets
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10.3 Areas of Circles and Sectors Notes
Area of a Circle:
Circumference of a Circle:
Guided Practice Your Turn
Find area and circumference.
11. 12.
Area of a Sector:
Guided Practice
Find the area of the shaded sector. Round to the nearest tenth.
1. 2.
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Your Turn
3. 4.
Guided Practice
5. 6.
Geometry Unit 10 & 11 Note Sheets
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10.4 Areas of Regular Polygons and Composite Figures Notes
Guided Practice
Area of a Regular Polygon
𝑆𝑜
ℎ𝐶𝑎
ℎ𝑇𝑜
𝑎
Guided Practice
Find the area of each regular polygon.
5.
Geometry Unit 10 & 11 Note Sheets
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6.
7. s = 6.62
Your Turn
8.
9. a = 7.28
s = 10.58
Geometry Unit 10 & 11 Note Sheets
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Find area of Composite Figures
Guided Practice
10. 11.
Your turn
12.
Geometry Unit 10 & 11 Note Sheets
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10.5 Area of Nonrigid Transformations
Example 1:
Guided Practice 1: If EFGH ~ LMNO and the area of EFGH is 40 square inches, find the area of LMNO.
Example 2: The area of ΔABC is 98 square inches. The area of ΔRTS is 50 square inches. If ΔABC ~
ΔRTS, find the scale factor from ΔABC to ΔRTS and the value of x.
Geometry Unit 10 & 11 Note Sheets
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Guided Practice 2: The area of ΔTUV is 72 square inches. The area of ΔNOP is 32 square inches. If ΔTUV
~ ΔNOP, use the scale factor from ΔTUV to ΔNOP to find the value of x.
Example 3: CRAFTS Jonathon has a banner that measures 1.5 feet by 6 feet. He makes two additional
banners that measure 3 feet by 12 feet and 3 feet by 10 feet, respectively. Describe how the difference in
dimensions affects the areas of the banners.
Guided Practice 3: MODELS The area of one hood of a car is 35 square feet. The area of the hood of a
model is 6 square inches. If the car is 14 feet long, about how long is the model?
Geometry Unit 10 & 11 Note Sheets
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10.6 Surface Area Notes
Lateral Area and Surface Area of Prisms
lateral faces
lateral edges
base edges
altitude
height
Lateral Area of a Prism
Guided Practice
1. Find the lateral area of the prism. Round to the nearest tenth.
Surface Area of a Prism
Guided Practice
2. Find the surface area of the triangular prism.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
Find the surface area of the rectangular prism.
3. 4.
Lateral and Surface Area of Cylinder
axis
Lateral and Surface Area of Cylinder
lateral area
surface area
Find the lateral area and surface area of the cylinder. Round to the nearest tenth.
Guided Practice Your Turn
5. 6.
Geometry Unit 10 & 11 Note Sheets
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Lateral Area and Surface Area Pyramids
lateral faces
lateral edge
base edge
altitude
Lateral Area of a Regular Pyramid
Guided Practice Your Turn
Find the lateral area of the square pyramid.
1. 2.
Surface Area of a Regular Pyramid
Geometry Unit 10 & 11 Note Sheets
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Guided Practice Your Turn
Find the surface area of the pyramid to the nearest tenth.
3. 4.
Lateral Area and Surface Area of Cones
right cone
oblique cone
Lateral Area and Surface Area of Cones
Guided Practice Your Turn
Find the lateral area and surface area of the cone. Round to the nearest tenth.
5. 6.
Geometry Unit 10 & 11 Note Sheets
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11.1 Cross Sections of Solids of Revolution Notes
Cross Section
Guided Practice
Describe each cross section.
1.
2. 3.
Your Turn
4. 5.
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Solid of revolution:
Guided Practice
1.
Your turn
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11.2 Volumes of Prisms and Cylinders Notes Volume of a Prism
Guided Practice
1. Find the volume of the prism.
Your Turn
2. Find the volume of the prism.
Guided Practice Your Turn
3. Find the volume of the prism. 4. Find the volume of the prism.
Volume of a Cylinder
Guided Practice
1. Find the volume of the given cylinder. Round to the nearest tenth.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
2. Find the volume of the given cylinder. Round to the nearest tenth.
Cavalieri’s Principle
Guided Practice
3. Find the volume of an oblique hexagonal prism if the height is 6.4 centimeters and the base area is 17.3
square centimeters.
Your Turn
4. Find the volume of the oblique rectangular prism shown.
Guided Practice
5. Find the volume of the oblique cylinder. Round to the nearest tenth.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
6. Find the volume of the oblique cylinder. Round to the nearest tenth.
Guided Practice
7.
8.
Your Turn
9.
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11.3 Volumes of Pyramids and Cones Notes Volume of a Pyramid
Guided Practice
1. Find the volume of the pyramid. Round to the nearest tenth if necessary.
Your Turn
2. Find the volume of the pyramid. Round to the nearest tenth if necessary.
3. Find the volume of the pyramid. Round to the nearest tenth if necessary.
Guided Practice
4. At the top of the Washington Monument is a small square pyramid, called a pyramidion. This pyramid
has a height of 55.5 feet with base edges of approximately 34.5 feet. What is the volume of the
pyramidion? Round to the nearest tenth.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
5. At the top of a stone tower is a pyramidion in the shape of a square pyramid. This pyramid has a height
of 52.5 centimeters and the base edges are 36 centimeters. What is the volume of the pyramidion?
Round to the nearest tenth.
Guided Practice
6. A square pyramid has base edges that are 14 centimeters and a height of 8 centimeters. Describe how
each change affects the volume of the pyramid. (Hint: If you are having trouble find the volume of the
original cylinder and the changed cylinders and then find how the volume is changed.
a) The height is tripled.
b) The base edges are doubled.
c) Both the base edges and the height are tripled.
Volume of a Cone
Guided Practice
1. Find the volume of the cone. Round to the nearest tenth.
Geometry Unit 10 & 11 Note Sheets
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Your Turn
2. Find the volume of the cone. Round to the nearest tenth.
3. Find the volume of the cone. Round to the nearest tenth.
Guided Practice
4. A cone has a volume of 568 cubic centimeters. What is the volume of a cylinder that has the same
radius as the cone? Explain your reasoning.
Your Turn
5.
6.
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11.4 Spheres Notes Surface Area of Sphere
Guided Practice
7. 8.
Your Turn
9. 10.
Definitions:
Great Circle__________________________________________________________________________
Hemisphere__________________________________________________________________________
Volume of a Sphere
Geometry Unit 10 & 11 Note Sheets
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Guided Practice
1. Find the volume of the sphere. Round to the nearest tenth.
2. Find the volume of the hemisphere. Round to the nearest tenth.
Your Turn
3. Find the volume of the sphere. Round to the nearest tenth.
4. Find the volume of a hemisphere with a diameter of 6 feet. Round to the nearest tenth.
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11.6 Volume and Nonnrigid Transformations Notes
Similar Solids: _______________________________________________________________
Congruent Solids:_____________________________________________________________
Example 1:
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Example 2: The surface area of a small pyramid is 40 square centimeters. If the scale factor between the
small pyramid and a larger pyramid is𝟏
𝟑 , what is the surface area of the larger pyramid?
Guided Practice 2: Two similar cones have radii of 5 inches and
15 inches. What is the ratio of the volume of the smaller cone to the volume of the larger cone?
Example 3: Circular cone A and circular cone B are similar. The cones have radii of 10 millimeters and
15 millimeters, respectively. The volume of cone A is approximately 1047.2 cubic millimeters. Find the
volume of cone B.
Guided Practice 3: SOFTBALLS The softballs shown are similar spheres. If the radius of the larger
softball is 1.9 inches, find the radius of the smaller softball.
Example 4: CONTAINERS The containers below are similar cylinders. Find the height h of the smaller
container.
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11.7 Applying Measurements
Example 1: A. Find the population density of Rhode Island to
the nearest tenth.
B. Find the population of Delaware, given that the
Population density is 379.7 persons/mi. Example 2: A rectangular state park with a length of 2.7 miles and a width of 2.5 miles has a duck population of 2500 ducks. The park rangers want to build a new playground, but can only build the playground if the duck population density is greater than 420 ducks per square mile. Does the population density allow for the playground to be built?
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Example 3: A sphere has a radius of 3 feet. Its mass is 550 grams. Find the density of the sphere to the nearest tenth. Example 4: An artist is making a sculpture in the shape of a rectangular prism that is 3 meters long, 180 centimeters wide, and 0.5 meter tall. She wants to be sure that the finished sculpture has a density less than 1.5 grams per cubic centimeter. If she makes the sculpture with clay, it will have a mass of 3780 kilograms. If she makes the sculpture with glass, it will have a mass of 6,480,000 grams. Which material should she use?
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