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Composite FiguresA

Multi-Part Lesson

9-3PART B C D

Lesson 9-3 Composite Figures 519

Area of Composite FiguresPOOLS The dimensions of a

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8 m

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28 ft

14 ft4 ft 6 ft

2 ft

pool at the recreation center are shown.

1. Describe the shape of the pool. See margin.

2. How could you determine the area of the pool’s floor? Separate the shape into a rectangle and a trapezoid, find the area of each, and add to find the total area.

To find the area of a composite figure, separate it into figures with areas you know how to find. Then add those areas.

Find the Area of a Composite Figure

Find the area of the figure at the right.

6 in. 4 in.

10 in.

6 in.

The figure can be separated into a rectangle and a triangle. Find the area of each.

Area of Rectangle Area of Triangle

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10 in.

6 in.

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4 in.

4 in.

A = bh A = 1 _ 2 bh

A = 10 · 6 or 60 A = 1 _ 2 (4)(4) or 8 The base of the triangle is

10 - 6 or 4 inches.

The area is 60 + 8 or 68 square inches.

Find the area of each figure.

a.

4 ft

12 ft

10 ft 8 ft

60 ft2 b.

2.5 cm

1.5 cm

9.2 cm

31.4 cm2

Main IdeaFind the areas of composite figures.

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520 Chapter 9 Use Formulas in Geometry

POOLS The diagram of the pool from the beginning of the

lesson is shown below. Find the area of the pool’s floor.

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8 m

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9-25-07CS

28 ft

14 ft4 ft 6 ft

2 ft

The figure can be separated into a rectangle and a trapezoid.

The area of the rectangle is 28 × 14 or 392 square feet. The area of the trapezoid is 1 _

2 (2)(4 + 6) or 10 square feet.

So, the area of the pool’s floor is 392 + 10 or 402 square feet.

Find the area of the figure at the right.

The figure can be separated into a

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12 cm

12 cm

12 cm

15 cm

6 cm8 cm

square and a rectangle. The shared rectangle, however, will be counted twice if the areas are added, so the area of the small rectangle, 6 × 7 or 42, must be subtracted from the total.

The area of the square is 12 × 12 or 144 square centimeters.

The area of the rectangle is 15 × 12 or 180 square centimeters.

The sum of the areas is 144 + 180 or 324 square centimeters.

Since the small rectangle was counted twice, subtract its area from the total. 324 - 42 = 282

So, the area of the figure is 282 square centimeters.

c. DECKS Find the area of the d. Find the area of the figure

deck shown. 672 ft2 below. 65 ft2

20 ft

10 ft

20 ft

36 ft

14 ft14 ft

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6 ft

2 ft

1 ft8 ft

6 ft

7 ft

Real-World LinkThe largest swimming pool in the world is located in Chile. It is one kilometer in length and is equivalent to approximately 6,000 standard pools.

Real-World LinkThe largest swimming

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Lesson 9-3 Composite Figures 521

Find the area of each figure. Round to the nearest tenth if necessary.Example 1(p. 519)

1.

12 m

14 m

4 m

7 m

112 m2 2.

6 ft

15 ft

6 ft

104.1 ft2 3.

10 m

15 m4 m 4 m10 m

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145 m2

Examples 2 and 3(p. 520)

4. APARTMENTS The manager of an apartment

10 ft

5 ft12 ft 8 ft

25 ft

complex will install new carpeting in a studio apartment. The floor plan is shown at the right. What is the total area that needs to be carpeted?342.5 ft2

5. TILING The floor plan of a kitchen is shown at 6 ft 6 ft

16 ft

12 ft

2 ft

11 ft

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the right. If the entire kitchen floor is to be tiled, how many square feet of tile are needed? 188 ft2

= Step-by-Step Solutions begin on page R1. Extra Practice begins on page EP2.

Find the area of each figure. Round to the nearest tenth if necessary.Example 1(p. 519)

6.

7 cm

10 cm

15 cm 7

8 in.4 in.

8 in.

5.3 in. 8.

7 yd

5 yd

54.2 yd2

87.5 cm2 58.6 in2

9.10 mm

20 mm

257.1 mm2 10.

11.3 ft

8 ft 4.3 ft

11.

69.5 ft2 66.2 yd2

Examples 2 and 3(p. 520)

12. BLUEPRINTS On a blueprint, a rectangular room 14 ft

12 ft

14 feet by 12 feet has a semicircular sitting area attached with a diameter of 12 feet. What is the total area of the room and the sitting area?about 224.5 ft2

13. POOLS The diagram at the right gives 18 ft

36 ft

20 ft

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the dimensions of a swimming pool. If a cover is needed for the pool, what will be the approximate area of the cover? 592.83 ft2

7 yd 4 yd

5.2 yd

2 yd

5.2 yd

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522 Chapter 9 Use Formulas in Geometry

14. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–b.

Let’s just find the area of the larger circle and take out the area of the smaller circle!

a. Find the area of the dirt bike track. Use 3.14 for π. 3,061.5 ft2

b. Suppose it costs $4.99 to cover one square foot of the dirt bike track with dirt. How much will it cost to cover the track with dirt? Round to the nearest cent. $15,276.89

B 15 PAINTING The diagram shows one side

14.5 ft

22.8 ft

26.5 ft

of a storage barn.

a. This side needs to be painted. Find the total area to be painted. 467.4 ft2

b. Each gallon of paint costs $20 and covers 350 square feet. Find the total cost to paint this side once. Justify your answer. See margin.

CHALLENGE Describe how to separate each state into simpler figures. Then use these figures to estimate the area of each state. One square unit equals 2,400 square miles. Justify your answer.

16.

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NEVADA

17. See margin.

18. Describe how you would find

5 cm

7 cm

9 cmthe area of the figure shown at the right. Sample answer: Separate it into a rectangle and a triangle, find the area of each, and add.

16. Sample answer: Add the areas of a rectangle and a triangle. Area of rectangle: 3 × 4 = 12; Area of triangle: 1 _ 2 × 3 × 3 = 4.5;

12 + 4.5 = 16.5. So, an approximate area is 16.5 × 2,400 or 39,600 mi2.

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Lesson 9-3 Composite Figures 523

Find the perimeter of each figure. (Lesson 9-3A)

22.

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4.3 in.

4.3 in.

4.3 in.

4.3 in.

4.3 in.

4.3 in.

25.8 in. 23.

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3 ft

3 ft3 ft

3 ft3 ft

30 ft 24.

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6.6 cm

8 cm

4 cm4 cm4 cm

2.6 cm 29.2 cm

Find the area of each circle. Use 3.14 for π. Round to the nearest tenth. (Lesson 9-2D)

25. radius = 4.7 cm 69.4 cm2 26. radius = 12 in. 452.2 in2 27. diameter = 15 in. 176.6 in2

Practice

19. What is the area of the window shown? Use 3.14 for π. A

36 in.

48 in.

A. 2,236.68 in2 C. 508.68 in2

B. 1,728 in2 D. 168 in2

20. The shaded part of the grid represents the plans for a fish pond.

If each square on the grid represents 5 square feet, what is the approximate area of the fish pond? G

F. 175 square feet

G. 165 square feet

H. 150 square feet

I. 33 square feet

21. EXTENDED RESPONSE To promote recycling, the

80 ft

45 ft30 ft

15 ftsandboxground of the neighborhood playground shown is being covered by shredded tires. The sandbox will not be covered.

Part A What is the area, in square feet, of the shredded tire portion of the playground? 3,150 ft2

Part B If shredded tires cost $2.99 per square foot, at the required depth, how much will it cost to cover the playground? $9,418.50

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