ACTIVITY Name: Date: F-3 Finding Area of Complex · PDF fileF-3 Finding Area of Complex...

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c.Name: Date: AC T I V I TY

Use both the addition and subtraction methods to find the area of the figures below.

1. Addition Method

Subtraction Method

2. Addition Method

Subtraction Method

3. Explain how you found the area using the subtraction method for Exercise 2.

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5 cm

3 cm3 cm

3 cm

4 cm4 cm

12 cm

10 cm

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8 in.

7 in.6 in.

6 in.

10 in.

16 in.

Math Word

complex figure

F-3 Finding Area of Complex Figures

sixty-three

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115 8

12A = 63 63

57-66_WA_Gr3_AdlLsn_Onln.indd 63 5/22/09 11:52:23 AM

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Match each math sentence with the correct division of the complex figure below.

UF-040A-106391

6 in.4 in.

13 in.

12 in.

UF-041A-106391 UF-042A-106391 UF-043A-106391 UF-044A-106391

A B C D

4. (6 × 3) + (7 × 7) + (13 × 5) 5. (6 × 3) + (6 × 5) + (7 × 12)

6. (13 × 12) – (6 × 4) 7. (13 × 3) + (7 × 4) + (13 × 5)

Finding AreaFind an object that is a complex figure in your classroom to add to your table. Use color tiles to find the area. Then use a ruler. Compare your results.

3 in.

5 in.

64

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P = 64

5

5 10

205 5

7sixty-four

57-66_WA_Gr3_AdlLsn_Onln.indd 64 5/22/09 11:52:28 AM

macmillanmh.commacmillanmh.com

Find the area of the shaded region.

So, the area of the shape is 48 square units.

Find the area of the shaded region.

A B

Use Models to Find Areas of Composite ShapesArea is measured in square units. You have used squares to find the area of rectangles and squares. You can also find the area of other shapes.

C

Main IdeaI will explore area.

8-3Multi-Part Lesson

Area of Composite Shapes

PART

One Way

Step 1 Count the square units.

The shape shows that there are 48 square units.

C08-093A-112056

Another Way

Step 1 Decompose the shape into rectangles and squares.

The shape can be broken into two rectangles and one square.

Step 2 Find the area of the parts. Then add them together.

3 × 5 = 153 × 3 = 9

6 × 4 = 24

15 + 24 + 9 = 48

396 Chapter 8 Find Area

C08-094A-112056

396-397_WA_Gr3_AdlLsn_Onln.indd 396 5/22/09 2:30:15 PM

About It 1. How else could you decompose the shape into rectangles?

2. How would that affect the area?

3. Why is it helpful to decompose shapes into rectangles?

4. On a piece of grid paper, shade in squares to make a picture. Find the area of the shape.

5. Why is the area of the shape in the activity labeled square units?

and Apply It

Find the area of each shape.

6. 7.

C08-099A-112056 C08-100A-112056 8. 9.

C08-101A-112056 C08-102A-112056 10. Which two exercises above have the same

area? Explain.

Lesson 8-3 Area of Composite Shapes 397


C

Multi-Part Lesson

8-3PART

Area of Composite Shapes

A B

Main IdeaI will find the area of composite shapes.

New Vocabulary composite shape

Find Areas of Composite ShapesA composite shape is made up of two or more shapes. To find the area of a composite shape, break it into smaller parts.

POOLS Drew is staying at a hotel that has the swimming pool shown. Drew wants to know the area of the pool. Find the area of the swimming pool at Drew’s hotel.

Step 1 Break up the figure into smaller parts. Look for rectangles and squares.

Step 2 Find the area of each part.

Step 3 Add the areas.

The area is 72 + 100 or 172 square meters.


SquareA = side × sideA = s × sA = 10 m × 10 mA = 100 sq m

RectangleA = length (base) × width (height)A = � × wA = 12 m × 6 m

A = 72 sq m


Area of a Composite Shape

Find the area of the compositeshape.

Step 1 Break up the shape into smaller parts. Look for rectangles and squares. This shape can be broken into 1 rectangle and 2 squares.

Step 2 Find the area of each part.

Rectangle Square A = length × width A = side × side A = 12 ft × 2 ft A = 3 ft × 3 ft A = 24 square feet A = 9 square feet

Step 3 Add the areas. 24 + 9 + 9 = 42

So, the area of the shape is 42 square feet.

Area of a Composite Shape

Find the area of each shape. See Examples 1 and 2 (pp. 398–399)

1. 2. 3.

4. What is the area of the garden shown at the right?

5. Refer to Exercise 4. When finding the area of the garden, what two shapes did you look for?



Find the area of each shape. See Examples 1 and 2 (pp. 398–399)

6. 7. 8.

9. 10. 11.

12. Courtney is playing miniature golf. What is the area of the entire shape?

13. What is the area of the desktop?

PRACTICEEXTRASee page R25.PRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEPRACTICEEXTRA

See page R25.

The builders of Fort Jefferson at Dry Tortugas National Park in Florida began in 1846. It was supposed to house large cannons, but was never completed.

14. Draw a picture to show how you could decompose a hexagon to find the area of Fort Jefferson.

15. Trace a hexagon pattern block on a centimeter grid paper. Count the squares to estimate the area.



Practice

16. OPEN ENDED Draw and label two composite shapes that have the same area but have different perimeters.

17. CHALLENGE Find the area of the shaded shape in units.

18. Create a word problem about a real-world situation involving perimeter and area of a composite shape.

Choose the better estimate. (Lesson 8-2E)

21. doormat 22. dining room table 23. bathroom tile6 square inches or 2 square feet or 16 square inches or 6 square feet 2 square yards 16 square yards

24. Pia plays 32 minutes each soccer game and has 15 games during the season. Her older sister plays 28 minutes each soccer game and has 18 games in her season. How many more minutes does Pia’s sister play than Pia? (Lesson 8-2D)


19. Which equation below represents the area (A) of the square in square inches?

A. 7 = A × 7

B. A = (2 × 7) + (2 × 7)

C. A = 7 × 7

D. A = 7 × 4

20. Which statement about the shape is true?

F. The area is equal to the perimeter.

G. The perimeter is greater than the area.

H. The perimeter 38 centimeters.

I. The area is 48 square centimeters.


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