Name
LESSON
Date
Class
Problem Solving
10-6 Area of Irregular and Composite Figures
Write the correct answer.
1. Explain how to find the area of
the composite figure below. Then
find the area.
2. Mr. Bemis carpets the living room
shown below. If he pays $20 per
square meter, what is the total cost
of the carpet?
10 ft
5m
10 ft
25 ft
6m
3m
20 ft
11 m
4. A figure is made of a rectangle
and an isosceles right triangle. The
rectangle has sides of 6 in. and 3 in.
One of the short sides of the
rectangle is also one of the legs of
the right triangle. What is the total
area of the figure?
3. A figure is made of a square and a
semi-circle. The square has sides of
16 cm each. One side of the square is
also the diameter of the semi-circle.
What is the total area of the figure?
Choose the letter of the correct answer.
4m
5. Norene builds the deck at the right.
The area of the deck is 10 m2 greater
than was originally planned. What is
the area of the deck?
A 110 m2
C 66 m2
D 56 m2
B 76 m2
10 m
2m
10 m
6. The grid to the right shows a
swimming pool. Each square
represents 1 square meter. What is
the best estimate of the area of the
swimming pool?
F 45 m2
H 37 m2
G 41 m2
J 32 m2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
50
Holt Mathematics
Problem Solving
LESSON
10-6 Area of Irregular and Composite Figures
Challenge
LESSON
10-6 Figure it Out!
Write the correct answer.
Sometimes there is more than one way
to find the area of a composite figure.
12 m
1. Explain how to find the area of
the composite figure below. Then
find the area.
10 m
8m
2. Mr. Bemis carpets the living room
shown below. If he pays $20 per
square meter, what is the total cost
of the carpet?
10 ft
22 m
5m
10 ft
Another Way
One Way
25 ft
10 m
10 m
12 m
8m
20 m
8m
12 m
22 m
22 m
A(rectangle) 10 8 80 ft2
1
A(trapezoid) 2 12 (20 8) 168 ft2
Another Way
One Way
21 ft
21 ft
9 ft
30 ft
738 ft2
Area 2.
6m
6m
11 m
356.48 cm2
Area 4m
6m
Choose the letter of the correct answer.
738 ft2
11 m
7m
7m
7m
6m
12 m
Area 96 m2
Area 96 m2
6 ft
4 ft
6 ft
14 ft
10 ft
16 ft
10 ft
4 ft
8 ft
Area 18 ft
18 ft
220 ft2
Area 220 ft2
49
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
10 m
2m
10 m
6. The grid to the right shows a
swimming pool. Each square
represents 1 square meter. What is
the best estimate of the area of the
swimming pool?
F 45 m2
H 37 m2
G 41 m2
J 32 m2
10 ft
10 ft
10 ft
4m
5. Norene builds the deck at the right.
The area of the deck is 10 m2 greater
than was originally planned. What is
the area of the deck?
A 110 m2
C 66 m2
D 56 m2
B 76 m2
6m
7m
12 m
22.5 in.2
6 ft
36 ft
6 ft
27 ft
15 ft
6 ft
6 ft
16 ft
4. A figure is made of a rectangle
and an isosceles right triangle. The
rectangle has sides of 6 in. and 3 in.
One of the short sides of the
rectangle is also one of the legs of
the right triangle. What is the total
area of the figure?
21 ft
9 ft
9 ft
3.
right triangle; 325 ft
12 ft
9 ft
6 ft
2
3. A figure is made of a square and a
semi-circle. The square has sides of
16 cm each. One side of the square is
also the diameter of the semi-circle.
What is the total area of the figure?
Show two different ways to find the area of each figure.
12 ft
$1,260
figure into a rectangle and a
A(figure) 80 168 248 ft2
A(figure) 176 72 248 ft2
11 m
Possible answer: Divide the
1
A(triangle) 2
12 12 72 ft2
3m
20 ft
8m
A(rectangle) 22 8 176 ft2
1.
6m
12 m
12 m
Holt Mathematics
50
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Puzzles, Twisters, & Teasers
LESSON
10-6 What’s Bugging You?
Reading Strategies
LESSON
10-6 Draw a Picture
Each square represents 1 square foot. Estimate the area of
each figure. Circle the letter next to the better estimate.
Sometimes a composite figure is made of shapes that you know,
such as rectangles, triangles, or semi-circles.
You can draw a line to break a composite figure into other shapes.
Then you can use those shapes to help you find the area.
16 ft
1.
2.
16 ft
10 ft
10 ft
8 ft
8 ft
32 ft
24 ft
D 23 ft
22 ft
32 ft
N 16 ft
F 11 ft2
I 26 ft2
2
2
Next, find the area of each figure. Circle the letter next to your answer.
3.
Answer each question.
3m
4.
2m
5.
2 ft
2 ft
2m
1. A dashed line has been drawn through the figure. What two
shapes does the dashed line create?
3m
12 m
6 ft
6m
a rectangle and a right triangle
12 m
4m
4 ft
16 m
2. How can you find the area of the rectangle?
A 54.28 ft
L 38 m2
Use the formula, area length width.
R 42 m
E 60.56 ft2
2
3. What is the area of the rectangle?
6.
80 ft2
7.
2m
3m
2
E 168 m2
8.
8 ft
4m
2m
4. How can you find the area of the right triangle?
1
Use the formula, area base height.
2
O 160 m
2
6m
9m
8 ft
3m
6m
6m
4m
18 m
5. What is the area of the right triangle?
264 ft2
S 89.12 ft2
L 60 m
Y 114.24 ft
A
7. What is the total area of the composite figure?
344 ft2
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
2
What kind of insect breathes fire?
Add the area of the rectangle to the area of the right triangle
51
F 126 m
2
B 144 m2
Write the circled letters above the problem numbers to solve the riddle.
2
6. How can you use the area of the rectangle and the area of the
right triangle to find the total area of the composite figure?
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
H 52 m2
Holt Mathematics
D
R
A
1.
3.
4.
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All rights reserved.
136
G
O
N
F
L
Y
5.
2.
8.
6.
7.
52
Holt Mathematics
Holt Mathematics