Msm1 fl ch09_04(2)

9-4 Area of Composite Figures
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes

40 cm2
216 ft2
64 cm2
78.5 in2
Warm Up
Find each area. Round to the nearest tenth, if
necessary.
1. a rectangle with length 10 cm and width 4 cm
2. a parallelogram with base 18 ft and height 12 ft
3. a triangle with base 16 cm and height 8 cm
4. a circle with radius 5 in.

Problem of the Day
Four squares are placed in a row,
adjacent to one another. The square on
the far left is 12 inches on a side. The
perimeter of each of the other squares
is half of the one to its left. What is the
perimeter of the combined figure?
69 in.

MA.6.G.4.2 Find the…areas of composite
two-dimensional figures…using various
strategies.
Also MA.6.A.3.4
Sunshine State Standards

Additional Example 1A: Finding the Area of
Composite Figures by Adding
Find the shaded area. Round to the nearest
tenth, if necessary.
A = bh
A = 12 • 6
A = 72 m2
area of the rectangle:
Divide the figure into a rectangle
and a trapezoid.

Additional Example 1A Continued
8 m
area of the trapezoid:2 m
6 m
2 m
6 m
A = h(b1 + b2
)
1
2
__
A = 2(4 + 2)
1
2
__
A = (12)
1
2
__
A = 6 m2
Add the area of the rectangle and the area of the
trapezoid.
total area: A = 72 + 6 = 78 m2
.
4 m

Additional Example 1B: Finding the Area of
Composite Figures by Adding
A = bh
A = 20 • 8
A = 160 in2
12 in.
20 in.
8 in.
and a semicircle.
8 in.8 in.

area of the semicircle:
A = (πr2
)
1
2
__
A ≈ (3.14 • 42
)
1
2
__
A ≈ (50.24)
1
2
__
A ≈ 25.1 in2
Additional Example 1B Continued
12 in.
20 in.
8 in.
8 in.
semicircle.
total area: A = 160 + 25.1 = 185.1 in2
.

A = bh
A = 8 • 9
A = 72 yd2
Check It Out! Example 1A
and a triangle.
10 yd
9 yd
8 yd

Check It Out! Example 1A Continued
area of the triangle:
A = bh
1
2
__
A = (2 • 9)
1
2
__
A = (18)
1
2
__
A = 9 yd2
triangle.
total area: A = 72 + 9 = 81 yd2
10 yd
9 yd
8 yd

Check It Out! Example 1B
A = bh
A = 22 • 10
A = 220 m2
12 m
22 m
and a semicircle.
10 m
10 m

area of the semicircle:
A = (πr2
)
1
2
__
A ≈ (3.14 • 52
)
1
2
__
A ≈ (78.5)
1
2
__
A ≈ 39.3 m2
Check It Out! Example 1B Continued
semicircle.
total area: A = 220 + 39.3 = 259.3 m2
12 m
22 m
10 m
10 m

Additional Example 2: Finding the Area of
Composite Figures by Subtracting
Find the shaded area.
A = bh
A = 12 • 9 = 108 ft2
Area of the rectangle: Area of the triangle:
A = bh
1
2
__
A = • (6)(7)
1
2
__
A = • 42 = 21 ft2
1
2
__
Shaded area:
Subtract the area of the triangle
from the area of the rectangle.
A = 108 – 21 = 87 ft2
5 ft
12 ft
6 ft
9 ft

Check It Out! Example 2
Find the shaded area.
A = bh
A = 16 • 8 = 128 in2
Area of the rectangle: Area of the triangle:
A = bh
1
2
__
A = • (5)(7)
1
2
__
A = • 35 = 17.5 in2
1
2
__
Shaded area:
Subtract the area of the triangle
from the area of the rectangle.
A = 128 – 17.5 = 110.5 in2
9 in.
16 in.
5 in.
8 in.

Additional Example 3: Landscaping Application
What is the area of the room
floor shown in the figure?
Round to the nearest tenth.
To find the area, divide the composite figure into
a square, a rectangle, and a semicircle.
6 ft
6 ft
12 ft12 ft
18 ft

Additional Example 3 Continued
A = s2
A = 62
= 36 ft2
Area of the square:
6 ft
6 ft
12 ft12 ft
A = bh
A = 18 • 6 = 108 ft2
Area of the rectangle:
A = πr2
1
2
__
A ≈ • 3.14 • (9)2
1
2
__
A ≈ (254.34)
≈ 127.17 ft2
1
2
__
Area of the semicircle:
18 ft

Additional Example 3 Continued
6 ft
6 ft
12 ft12 ft
18 ft
The area of the room is approximately 271.2 ft2
.
A = 36 + 108 + 127.17 = 271.17 ft2
Area of the room:

Check It Out! Example 3
What is the area of the stage
To find the area, divide the composite figure into
a square, a rectangle, and a semicircle.
5 ft
5 ft
10 ft10 ft
15 ft

Check It Out! Example 3 Continued
A = s2
A = 52
= 25 ft2
Area of the square:
5 ft
5 ft
10 ft10 ft
A = bh
A = 15 • 5 = 75 ft2
Area of the rectangle:
A = πr2
1
2
__
A ≈ • 3.14 • (7.52
)
1
2
__
A ≈ (314)
≈ 88.3 ft2
1
2
__
Area of the semicircle:
15 ft

Check It Out! Example 3 Continued
5 ft
5 ft
10 ft10 ft
15 ft
The area of the room is 188.3 ft2
.
A = 25 + 75 + 88.3 = 188.3 ft2
Area of the room:

Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems

Lesson Quiz: Part l
Find the shaded area of each figure. Round
to the nearest tenth, if necessary.
1.
2.
111 ft2
188.9 mm2
5 ft
3.
45.9 in2

Lesson Quiz: Part ll
4. The figure gives the dimensions of a backdrop
for a school play. Find the area of the backdrop.
97 ft2

1. Find the shaded area of each figure. Round to
the nearest tenth, if necessary.
A. 40 ft2
B. 54.1 ft2
C. 14 ft2
D. 68.3 ft2
Lesson Quiz for Student Response Systems
5 ft
8 ft
2 ft

Msm1 fl ch09_04(2)

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