Name:
AC T I V I T Y
F-3
Date:
Finding Area of Complex Figures
Use both the addition and subtraction methods
to find the area of the figures below.
Math Word
complex figure
1.
Addition Method
5 cm
3 cm
3 cm
10 cm
3 cm
4 cm
Subtraction Method
4 cm
12 cm
2.
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6 in. Addition Method
10 in.
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8 in.
Subtraction Method
7 in.
6 in.
16 in.
3. Explain how you found the area using the subtraction method
for Exercise 2.
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sixty-three
5
11
12
8
A = 63
63
Match each math sentence with the correct division of
the complex figure below.
3 in.
6 in.
4 in.
12 in.
5 in.
13 in.
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B
C
D
4. (6 × 3) + (7 × 7) + (13 × 5)
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5. (6 × 3) + (6 × 5) + (7 × 12)
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6. (13 × 12) – (6 × 4)
7. (13 × 3) + (7 × 4) + (13 × 5)
Finding Area
Find 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.
5
64
5
5
7
20
10
5
sixty-four
P = 64
Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A
Multi-Part Lesson
8-3
PART
Main Idea
I will explore area.
Area of Composite Shapes
A
B
C
Use Models to Find Areas
of Composite Shapes
Area 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.
macmillanmh.com
Find the area of the shaded region.
One Way
Step 1
Count the square units.
The shape shows that
there are 48 square units.
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Another Way
Step 1
Decompose the shape
into rectangles and squares.
The shape can be broken
into two rectangles and
one square.
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Step 2
Find the area of the parts. Then add them
together.
3 × 5 = 15
3×3=9
6 × 4 = 24
15 + 24 + 9 = 48
So, the area of the shape is 48 square units.
396 Chapter 8 Find Area
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.
8.
10.
7.
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area? Explain.
9.
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Which two exercises above have the same
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Lesson 8-3 Area of Composite Shapes
397
Multi-Part Lesson
8-3
Area of Composite Shapes
PART
Main Idea
I will find the area of
composite shapes.
New Vocabulary
composite shape
A
B
C
Find Areas of
Composite Shapes
A 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.
Rectangle
A = length (base) × width (height)
A=
×
w
A=
12 m
×
6m
A = 72 sq m
Step 3
Square
A = side × side
A= s
× s
A = 10 m × 10 m
A =100 sq m
Add the areas.
The area is 72 + 100 or 172 square meters.
398 Chapter 8 Find Area
Area of a Composite Shape
Find the area of the composite
shape.
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
A = length × width
A = 12 ft × 2 ft
A = 24 square feet
Step 3
Square
A = side × side
A = 3 ft × 3 ft
A = 9 square feet
Add the areas.
24 + 9 + 9 = 42
So, the area of the shape is 42 square feet.
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?
Lesson 8-3 Area of Composite Shapes
399
EXTRA
%
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2A
0R
P
See page R25.
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?
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.
400 Chapter 8 Find Area
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.
Practice
19. Which equation below represents
the area (A) of the square in
square inches?
20. Which statement about the shape
is true?
F. The area is equal to the
perimeter.
A. 7 = A × 7
B. A = (2 × 7) + (2 × 7)
C. A = 7 × 7
G. The perimeter is greater than
the area.
D. A = 7 × 4
H. The perimeter 38 centimeters.
I. The area is 48 square
centimeters.
Choose the better estimate. (Lesson 8-2E)
21. doormat
6 square inches or
6 square feet
22. dining room table
2 square feet or
2 square yards
23. bathroom tile
16 square inches or
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)
Lesson 8-3 Area of Composite Shapes
401