Measurement in Two and Three Dimensions Math A College Prep

Module #7 Homework 2017 - 2018

Created in collaboration with Utah Middle School Math Project A University of Utah Partnership Project

San Dieguito Union High School District

7.0A Homework: Using the Area Formulas Name:

Period:

Find the area of the following triangles. 1.

2.

3.

5.2 in 3 in

6 in

Find the area of the following parallelograms. 4.

5.

6.

Find the area of the following trapezoids. 7.

8.

9.

4 mm

7 5 mm

3 mm

4.2 8 mm

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3.2 3

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7.1A Homework: Perimeter and Area Problem Solving* Name:

Period:

Answer each of the questions below. 1. What is the least number of tiles you can add to the figure below to create a shape with a perimeter of 16 units? Note: When adding a tile, the new tile must share at least one side with the original shape; each tile is 1 unit by 1 unit. Hint: draw the figure on a separate sheet of paper and cut out “tiles” to move them around.

2. Use the original figure given above to answer a-d. Draw your answers. Note, an answer of just “yes” or “no” is not sufficient. Use pictures or words to justify your answer. a. Can you add a tile to this figure to increase the perimeter by 1? If so, draw the new figure.

b. Can you add a tile to this figure to increase the perimeter by 2? If so, draw the new figure.

c. Can you add a tile to this figure to increase the perimeter by 3 (remember the new tile must share at least one side with the original shape)? If so, draw the new figure.

d. Can you add a tile to this figure so that the perimeter doesn’t change? If so, draw the new figure.

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You have a supply of unit tiles. 3. Can you make more than one shape with the same perimeter as #1, but with a different area (adding tiles)? Show your ideas with grid paper.

4. Can you make more than one shape with the same area (same number of tiles) as #1, but with a different perimeter? Show your ideas with grid paper.

5. If you pick any whole number between 12 and 24, and use that many unit tiles, can you make a shape where the area and perimeter are equal (ignoring the fact that perimeter is in units and area is in units2)? Show your ideas.

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Spiral Review: 6. Find the area of each of the following shapes. Show the formula you are using, and substitutions. Label your answer. Leave your answers in terms of 𝜋 when applicable. a. b.

c.

d.

7. Solve: −8 < −3𝑚 + 10

9. Write

! !

8. Solve: −12 > 3𝑥

as a percent and decimal.

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7.1B Homework: Areas of Irregular Shapes* Name:

Period:

1. The following shapes have been drawn on square dot paper. The distance between each dot represents one unit. Write your answers in the table below. Use 𝜋 ≈ 3.14. A

B C

E D

F

G H

I J

A:

B:

C:

D:

E:

F:

G:

H:

I:

J:

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Solve the following area problems. Show all of your calculations. 2. A rectangular lap pool with a length of 40 ft. and a width of 15 ft. is surrounded by a 5-ft. wide deck. a. Find the area of the deck.

b. Draw a picture of the deck if the deck is extended 3 feet more in every direction, then find the area of the new deck.

3. Johona is building a deck off the back of her house. To the right is a sketch of it. She will need to have a full concrete foundation below the deck. Find the area of the concrete foundation.

9 ft

2 ft

6 ft

15 ft

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4. Laura is painting a sign for the new Post Office. She will paint the triangular portion blue and the lower rectangular portion red. a. Find the area of sign that she will paint blue.

b. What percent of the sign will be in blue? Round to the nearest hundredth of a percent.

Spiral Review 5. Simplify the following expressions: a. −60 + 5𝑥 − 1 − 17𝑥

b. 9 5 − 𝑥 + 3𝑥 − 8

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7.1C Homework: Areas of Irregular Shapes and Expressions* Name:

Period:

Answer the following questions writing your answer in simplest form.

18 m

2. Find the perimeter and area of the region. Round to the nearest hundredth. (Use 𝜋 ≈ 3.14) 4m

1. Find the area of the region.

19 m

24 m

3. A stage design is illustrated in the figure to the right. a. Find the area of the stage.

b. What is the area of just the rectangular portion of the stage?

c. What percent of the stage is the rectangular portion? Round to the nearest hundredth of a percent.

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4. Rachel is painting a sign for the new Health Center. a. Find the area of sign.

b. Suppose Rachel decides to paint the rectangular portion (the part shown below the dotted line) of the sign blue. What percent of the sign would be blue?

For #5-9, answer each question. Simplify each answer completely. 5. Write an expression for the area.

7. Write an expression for the area.

8n 17 2n 13 6n

6. Find the perimeter of this region:

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8. Write an expression for the area. (Reminder: Arrows mean lines are parallel.)

9. Write an expression for the area of the unshaded region. Leave in terms of 𝜋.

8 cm

x cm 15 cm

x+6 x+2

5

Spiral Review 10. Write and solve a proportion to solve this problem: What percent of 27 is 3?

11. Two angles are supplementary. One angle is 49 degrees less than the other. What are the measures of each angle?

12. Write 0.672 as a percent.

!

13. Sam has lots of bracelets. Her friend gives her 3 more bracelets. Then she sells of the bracelets. Write ! two different equivalent expressions showing how many bracelets Sam has left.

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7.1D Homework: Problem Solving with Area* Name:

Period:

1. Wallpaper comes in rolls that are 60 feet long and 2 feet wide. How many rolls of wallpaper will it take to cover 700 square feet?

2. A rectangular garden has an area of 45 square feet. One of the sides is 6 feet. a. What is the other side?

b. You want to put a fence around it. How long will the fence need to be?

c. You decide you want to increase the length of each side by a scale factor of 3.2. What are the new dimensions of your garden?

d. What is the area of your new garden?

3. A 12 foot by 16 foot rectangular office is being sectioned off into two triangular areas so that desks can be placed in opposite corners. The diagonal of the office is 20 feet. The manager needs a dividing curtain to hang from the ceiling around one of the triangles. a. How long does the curtain need to be?

20

12

16

b. The carpet in each section will be a different color. How many square feet of carpet will be needed to cover each triangular section?

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4. Your neighbor’s backyard lawn is shaped like a rectangle. The length of the lawn is 38.2 feet and the width measures 32.6 feet. He will pay you $0.04 per square foot for mowing and $0.11 per foot for trimming all the edges. How much will you get paid total for mowing and trimming? Remember to show all your work. a. What is the area to be mowed?

b. How much are you paid to mow? c. What is the perimeter to be trimmed?

d. How much are you paid to trim? e. What is the total you are paid for both mowing and trimming?

5. You’re the manager of a county recreation center that has a 50 by 25 meter rectangular pool. Currently, there is an 1.5 meter cement walkway around the pool (see diagram). The community is concerned about the safety of the walkway and would like to cover it with a non-slip rubber substance that costs $78 a square meter to be installed. The county has budgeted $15,000 for the project. Is that enough money to cover the walkway? Explain you answer.

6. A hot tub is surrounded by a square deck as pictured to the right. What is the area of the deck? Round to the nearest hundredth.

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7. Cristian is building a rectangular garden in his backyard. The width of the garden is set at 29 inches. He wants the fence to be 5 inches longer than the garden on each side. If he wants the area enclosed by the fence to be 2028 square inches, how long should the garden be?

Spiral Review: 8. Eugene’s math class has 20 boys and 10 girls. If the teacher draws a student’s name at random for a candy bar, what is the probability Eugene will be chosen? What is the probability that a girl will be chosen?

9. Simplify the following: a. −1 −4 −7 − 28

!

!

!

!"

d. − +

−

! !

b. −14 − −13 + 28

!

!

!

!

!"

!

e. ( )( )( )

SDUHSD Math A College Prep Module #7 – HOMEWORK 2017-2018

c. 37 + −49 2

f.

−

!" !"

÷

! !

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Section 7.1 Review* Name:

Period:

For #1-2, find the area of the following figures. 1.

2.

3.

Find the perimeter and area.

4.

Find the perimeter and area.

7 cm

5 cm

3 cm

4 cm

2.5 cm

4.1 cm 4 cm

11 cm

5.

Phillip is mowing his backyard. His backyard is oddly shaped, and has an 8 ft by 8 ft square pond in his backyard. What is the total area Phillip will be mowing?

a. b. c. d.

64 square feet 106 square feet 336 square feet 400 square feet

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6.

Find the perimeter and area of the shape below. Document all work.

13.9'

13'

7.

Write simplified expressions for the perimeter and area of the shape below.

9

15'

6

2n 5n

10'

17'

8.

20

Find the area and perimeter of the shaded region Round your answer to the nearest tenth.

9.

A soybean farmer uses an irrigation system in which a 150 ft. straight pipe shown at right travels in a circle around a well as shown in the figure below.

12 mm

20 mm

How many square feet of the field are irrigated? Round to the nearest whole number.

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7.2A Homework: 2D Plane Sections of Solids* Name:

Period:

Use your knowledge of each three-dimensional object to answer the following questions. Cubes 1. How many faces does a cube have?

2. What do you know about each face of a cube?

3. How many edges does a cube have?

4. How many vertices does a cube have? 5. What shape is the base? Rectangular Prisms 6. How many faces does a rectangular prism have?

7. How many edges does a rectangular prism have?

8. How many vertices does a rectangular prism have?

9. What shape is the base? 10. How are a rectangular prism and a cube similar and different?

Spheres 11. How many edges and vertices does a sphere have? Does a sphere have a base?

12. What makes a sphere different from all the other 3D objects named above?

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For each plane-section described below, state the shape of the plane-section and its area. Refer to previous class activities, as needed. 13. Imagine cutting a cube parallel to its base. a. What shape is the plane section?

b. If you cut a 5 × 5 × 5 inch cube parallel to any face, what will the area of the plane section be?

14. Imagine a triangular prism: a. What shape is the plane section parallel to the base?

b. What shape is a plane section perpendicular to the base?

15. Imagine cutting a square based right pyramid parallel to the base. a. What shape is the plane section?

b. If the dimensions of the length and the width of the plane section are

3 3 in. and in., what is the area 2 2

of the plane section?

Spiral Review: 16. Find the perimeter and area of each figure below: a.

b.

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17. Solve and graph the following inequality:   −97 ≥ 4 19 − 2𝑥 + 3

18. Solve: 17𝑥 − 3 5𝑥 + 7 = −3  

19. Angel owes his mom $124. Angel made two payments of $41 to his mom. How much does Angel now owe his mother? Show your work.

20. Simone rolls a die 64 times. Approximately, how many times will she roll a 6?

21. Find the unit rate for BOTH units for the statement below: Izzy drove 357 miles on 10 gallons of gasoline.

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7.2B Homework: Nets, Surface Area, and Volume of 3D Objects* Name:

Period:

Look at each net below. (a). Trace and outline one base. (b). Name the object that is created when the net is folded. (c). Can you create congruent parallel plane sections (cross-sections)? If so, describe them. If not, explain why. NET

NET

1. a.

2. a.

b. Name the object that is created when the net is folded. Triangular Prism

b. Name the object that is created when the net is folded. Triangular Pyramid

c. Can you create congruent parallel plane sections (cross-sections)? If so, describe them. If not, explain why. Yes. Triangle base. All other faces are rectangles, so this can be turned any direction.

c. Can you create congruent parallel plane sections (cross-sections)? If so, describe them. If not, explain why. No. Triangular base. No matter how the object is oriented, there is no way to make parallel cuts that result in plane sections that are the same. 4. a.

3. a.

b. Name the object that is created when the net is folded. Square Pyramid

b. Name the object that is created when the net is folded. Hexagonal Prism

c. Can you create congruent parallel plane sections (cross-sections)? If so, describe them. If not, explain why. No. Triangular base. No matter how the object is oriented, there is no way to make parallel cuts that result in plane sections that are the same.

c. Can you create congruent parallel plane sections (cross-sections)? If so, describe them. If not, explain why. Yes. Hexagon base. All other faces are rectangles, so this can be turned any direction.

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5. Which of the following nets make a cube? a. b.

d.

c.

e.

f.

6. Each of the following nets can be folded to form a cube. After folding, what number will be directly opposite the 1? a. b.

1

4 5 6

2

1

6 2

3

3 5 4

Use the rectangular prism to the right for the next three problems. 7. Draw a net for the following shape and label the edges.

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8. Find the surface area.

9. Find the volume.

10. If the height of a square based prism is 13 in and its volume is 637 in3, what is the length of each side of the base?

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Use the triangular prism to the right for #11-13. 11. Draw a net for the shape and label the edges.

12. Find the surface area.

13. Find the volume.

Spiral Review: 14. On a map of New York City, with a scale of 1 inch= ½ mile, Central Park is 1 inch wide and 5 inches long. What is the area of the park?

15. Given the following table, find the indicated unit rate:

push-ups per day

Days Total Push-ups 2

30

4

60

29

435

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7.2C Homework: Growing and Shrinking Objects* Name:

Period:

For each of the following problems, find the necessary measurements to answer all the questions. 1. A mini cereal box has the following dimensions: 4.5 in by 6 in by 2 in. a. If all the dimensions are doubled, will it require double the amount of cardboard to make the box? Why or why not?

b. If all the dimensions are doubled, will it hold double the amount of cereal? Why or why not?

c. If one of the dimensions is doubled, will it require double the amount of cardboard to make the box? Why or why not?

d. If one of the dimensions is doubled, will it hold double the amount of cereal? Why or why not?

e. If all the dimensions are increased by 4 inches to: 8.5” by 10” by 6” how does this change the amount of cardboard needed to make the box?

f.

If all the dimensions are increased by a value of 4 inches, as described in “e”, how will this change the amount of cereal the box can hold?

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2. A container of chocolate milk mix has the following dimensions: a square base with sides of 6 in. and height 9 in. a. If all the dimensions are reduced by a scale factor of 13 , will it require a third the amount of materials to make the container? Why or why not?

!

b. If all the dimensions are reduced by a scale factor of , will it hold a third the amount of chocolate milk ! mix? Why or why not?

c. If the length of each side of the base is reduced by a scale factor of what are the new dimensions? _______________

1 3

but the height stays the same,

What is the new surface area? _______________ Find the volume of the reduced shape. ________________

Spiral Review: 3. Draw and describe the plane section that results from the following cut: a cylinder cut parallel to the base.

4. Katherine is visiting patients in a hospital. She visits 9 patients in 3 hours. She visits 18 patients in 6 hours. Is this situation proportional? If so, what is the unit rate?

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7.2D Homework: Surface Area and Volume of Composite Solids Name:

Period:

1. Calculate the surface area of the object to the right. (Not drawn to scale).

9 9

3

18

18

2. Chris made a solid by joining two identical rectangular prisms as pictured below. The overall dimensions of the composite solid are 20 cm by 18 cm by 15 cm. What is the surface area of a single prism?

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3. If a 3 cm cube is placed inside a box that is 10 cm by 5 cm by 8 cm, what is the volume inside the larger box that is outside the smaller box?

4. Calculate the volume of the object shown to the right. 12 in. 10 in. 5 in. 11 in.

3 in. 4 in.

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Section 7.2 Review* Name:

Period:

1. Draw and describe the plane section that results from the following cuts. a. A rectangular prism is cut b. A cube is cut perpendicular to parallel to the base. the base and parallel to a face.

c. A right pyramid is cut parallel to the base.

2. Find the surface area and volume of the following rectangular prism:

3. Use the triangular prism below for the next two questions.

a. Find the surface area of the prism.

b. Find the volume of the prism.

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4. For a rectangular prism with dimensions 8 cm by 15 cm by 2 cm: a. Find the surface area. b. Find the volume.

c. If the prism is scaled by a factor of 3, what is the new surface area?

d. If the prism is scaled by a factor of 4, what is the new volume?

5. Ellie is filling a sandbox for her son. The sandbox dimensions are 4 ft by 4 ft by 1 ft. How many cubic feet of sand does she need to buy to fill the sandbox?

6. The object below is made up of two rectangular prisms. What is the volume, in cubic feet, of the object?

a. b. c. d.

7. Which expression will allow Michael to correctly compute the surface area of a cube with sides 𝑥? a. 6𝑥 b. 12𝑥 c. 6𝑥 ! d. 𝑥 !

52 60 68 896

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8. The solid below was made by joining two blocks of wood. What is the surface area of the composite solid?

9. Cube A has a volume of 128 cm3. If the edge lengths of cube B are half the size of the edge lengths of cube A, what is the volume of cube B?

a. b. c. d.

16 cm3 32 cm3 64 cm3 Cannot be determined

10. Which of the following nets can be folded to form a square pyramid? Select all that apply. a. b. c.

11. This figure is a cube.

Select all figures that can be formed by a vertical slice perpendicular to the base of the cube. a. Rhombus b. Square c. Trapezoid d. Triangle

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12. The figure below is a right rectangular pyramid.

Select True or False for each statement describing the two-dimensional figure that results from slicing the figure above by a plane at various positions.

Statement a. A triangle is formed when the figure is sliced by a plane parallel to its base.

True

False

☐

☐

b. A trapezoid is formed when the plane is sliced by a plane not parallel to its base.

☐

☐

c. A rectangle is formed when the figure is sliced by a plane perpendicular to its base and containing the apex.

☐

☐

13. The dimensions of Hans’ turtle aquarium are 18 in by 18 in by 12 in. The dimensions of Anna’s rabbit cage are all twice the dimensions. a. Find the surface area and volume of each animal habitat.

b. Find the scale factor between the surface areas of each container.

c. Find the scale factor between the volumes of each container.

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