Geometry Unit 10 & 11 Note Sheets Date Name of …...Geometry Unit 10 & 11 Note Sheets 1 Date Name of Lesson 10.1 Areas of Parallelograms, Triangles 10.2 Areas of Trapezoids, Rhombi

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


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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


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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


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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.


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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).


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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


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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?


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10.3 Areas of Circles and Sectors Notes

Area of a Circle:

Circumference of a Circle:


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.


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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.


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6.

7. s = 6.62

Your Turn

8.

9. a = 7.28

s = 10.58


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Find area of Composite Figures

Guided Practice

10. 11.

Your turn

12.


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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.


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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?


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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.


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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.


5. 6.


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Lateral Area and Surface Area Pyramids

lateral faces

lateral edge

base edge

altitude

Lateral Area of a Regular Pyramid


Find the lateral area of the square pyramid.

1. 2.

Surface Area of a Regular Pyramid


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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


Find the lateral area and surface area of the cone. Round to the nearest tenth.

5. 6.


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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.


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.


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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.


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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



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.


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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.


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Your Turn



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


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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?

Documents

Geometry Unit 10 & 11 Note Sheets Date Name of …...Geometry Unit 10 & 11 Note Sheets 1 Date Name of Lesson 10.1 Areas of Parallelograms, Triangles 10.2 Areas of Trapezoids, Rhombi