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Multi-Part Lesson
9-3
PART
Composite Figures
A
Main Idea
Find the perimeter of a
composite figure.
New Vocabulary
perimeter
composite figure
glencoe.com
B
C
D
Perimeter of Composite Figures
MOVIE THEATERS One of the largest
movie theater screens is in St. Louis,
Missouri. The 500-seat theater
houses a 60-foot by 80-foot movie
screen that is nearly twice the size of
a traditional movie theater screen.
1. Suppose the theater owners
wanted to put a fabric border
around the screen. What would be the length of fabric? 280 ft
2. How did you find the distance around the screen?
3. How could you use multiplication and addition to find the
distance around the screen? Sample answer: Multiply the length by 2
and width by 2. Add the products.
Perimeter is the distance around a figure. Recall that a rectangle is
a four-sided figure with four right angles and the opposite sides
have equal lengths.
2. Sample answer: I
added the length of each
side.
Perimeter of Rectangles
Words
Symbols
Model
The perimeter P of a rectangle is
twice the sum of the base b and
height h.
h
b
P=b+b+h+h
P = 2b + 2h or 2(b + h)
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Find Perimeter of a Rectangle
Find the perimeter of the rectangle.
P = 2b + 2h
Perimeter of a rectangle
P = 2(7) + 2(13)
Replace b with 7 and h with 13.
P = 14 + 26 or 40 Multiply. Then add.
The perimeter is 40 yards.
13 yd
7 yd
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a. Find the perimeter of a rectangle with a base
of
7.6 centimeters and a height of 4.9 centimeters. 25 cm
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Composite Figures
Composite figures are also
sometimes called complex
figures or irregular figures.
A composite figure is made
of triangles, quadrilaterals,
semicircles, and other
two-dimensional figures.
semicircle
trapezoid
To find the perimeter of a composite figure, add the distances
around the closed figure.
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Find Perimeter of a Composite Figure
Find the perimeter of the figure.
4m
1.2 m
1m
Add all of the distances around
the composite figure.
1.2 m
4m
P = 1.2 + 1.2 + 4 + 1 + 4 Sum of all sides
P = 11.4 m
Add.
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The perimeter is 11.4 meters.
Find the perimeter of each figure.
b.
10.5 ft
5.5 ft
5.5 ft
5.5 ft
5.5 ft
43 ft
c.
5 cm
5 cm
6 cm
10.5 ft
28 cm
6 cm
6 cm
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GARDEN Find the perimeter of
the garden to the nearest tenth.
The distance around the
semicircle is unknown. So, you
need to find the circumference
of a circle.
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20 ft
x
12 ft
8 ft
15 ft
25 ft
semicircle
Step 1 Find the circumference of the circle.
C = πd
Circumference of a circle
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C = 3.14(15) Replace d with 15. Use 3.14 for π.
C ≈ 47.1
Multiply.
Step 2 Since you only need half of the circumference, divide by 2.
The distance around the semicircle is approximately 47.1 ÷ 2
or 23.6.
Step 3 Find the perimeter of the garden.
The perimeter of the garden is 20 + 12 + 8 + 25 + 23.6 or
88.6 feet.
Lesson 9-3 Composite Figures
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18 ft
d. POOLS Find the
perimeter of the pool
shown. 73.68 ft
12 ft
12 ft
18 ft
Find Missing Measures to Find
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Perimeter
Find the perimeter of the figure.
45 ft
Find the unknown lengths by breaking
the figure into two shapes.
40 ft
45 ft
15 ft
?
40 ft
35 ft
?
15 ft
5 ft
15 ft
30 ft
5 ft
The sum must
be 40 feet.
5 ft
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The sum must
be 45 feet.
So, the perimeter is 45 + 40 + 15 + 5 + 30 + 35 or 170 feet.
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56 cm
f.
5.2 mm
16 cm
e.
7 cm
12 cm
3.7 mm
3.1 mm
6.1 mm
8 cm
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Examples 1 and 4
(pp. 512, 514)
19.6 mm
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Find the perimeter of each figure.
1
2.
18 yd
2.9 cm
5 yd
46 yd
3.
12.6 cm
31 cm
18 m
20 m
88 m
11 m
24 m
Examples 2 and 3
(p. 513)
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4. FLAGS The flag of Ohio is the
only state
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flag that is not in the shape of a rectangle.
Find the perimeter of the flag. 16 f
3 ft
5 ft
1.5 ft
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1.5 ft
5 ft
514
Chapter 9 Use Formulas in Geometry
$"
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= Step-by-Step Solutions begin on page R1.
Extra Practice begins on page EP2.
Examples 1 and 2
(pp. 512–513)
Find the perimeter of each figure. Use 3.14 for π.
5.
164 yd
40 yd
6.
21 yd
21 yd
21 yd
1.5 m
2m
21 yd
7.
2m
2m
40 yd
2m
1.5 m
62.27 cm
17 cm
8.
14 m
1.5 m
1.5 m
67.68 in.
15 in.
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14 cm
14 cm
12 in.
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11 cm
15 in.
Example 3
(p. 513)
9. CARPENTRY Mr. Thomas wants to put a
5 ft
4 ft
baseboard in the room shown. Find the
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perimeter of the room to determine how
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many feet of baseboard he will need. 64 ft
10 ft
15 ft
12 ft
18 ft
10. NASCAR One of the shortest
professional racetracks is the
Bristol Motor Speedway in
Tennessee. Find the length, in
feet, of one lap of the track. 3,121.2 ft
Example 4
(p. 514)
Find the perimeter of each figure.
11.
12 yd
15 yd
106 yd
12.
$"
46.8 m
13 m
7.8 m
19 yd
17 yd
30 yd
B
4 yd
650 ft
$"
ft
580
4.3 m
3.1 m
2.6 m
13 BASKETBALL A basketball court measures 26 meters by 14 meters. Ten
meters of seating is added to each side of the court. Find the perimeter
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the rectangle enclosed by the court and the seating area. 160 m
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14. ALGEBRA Find the value of y given the perimeter
P. How many segments y units long are needed
for the perimeter? y = 9 cm; 6 segments
P = 54 cm
y
y
y
Lesson 9-3 Composite Figures
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C
15. OPEN ENDED Draw and label a composite figure made up of a
rectangle and semicircle with a perimeter between 100 and
200 centimeters. Find the perimeter.
16. CHALLENGE Find the perimeter of the figure at
the right.
17.
Describe how to find the
distance around a semicircle.
Practice
18.
8 in.
16 in.
GRIDDED RESPONSE Mao is framing
a picture. The picture frame is shown.
What is the perimeter of the outside of
the picture frame in inches?
10 in.
8 in.
16 in.
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19. Phillipe draws an equilateral triangle.
Next he draws a regular pentagon
with the same perimeter as the
triangle. How long is each side of the
regular pentagon?
1
1 2 in.
6.4 in.
6.4 in.
6.4 in.
8 in.
A. 32 in.
C. 6.4 in.
B. 25.6 in.
D. 3.84 in.
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$"
_
Find the area of each circle. Use 3.14 or 22 for π. Round to the nearest tenth if
7
necessary. (Lesson 9-2D)
20.
21.
19 yd
22.
47 ft
7
11 in.
23. TRACK AND FIELD The diameter of the circle that a shot-putter stands in is
22
7 feet. What is the circumference of the circle? Use _
for π. (Lesson 9-2B)
7
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24. POPULATION As the fastest growing county in the U.S., the population of
Flagler County, Florida, grew 10.7% in a recent year. Write 10.7% as a
decimal. (Lesson 5-2D)
25. TRAVEL While working in a toll booth, Russ recorded
the number of cars that had one passenger. Create a
line plot of the data. (Lesson 3-2D)
516
Number of Cars with One Passenger
32
45
34
41
39
36
34
40
39
33
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