This document provides examples and lessons on calculating the area of composite figures, which are figures made up of simple geometric shapes. It includes examples of finding the area by adding the areas of individual shapes, subtracting areas, and applications involving floor plans. The examples are presented with step-by-step workings. Quizzes are provided to assess understanding of calculating areas of composite figures.

1. 9-4 Area of Composite Figures
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes

2. 9-4 Area of Composite Figures
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.

3. 9-4 Area of Composite Figures
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.

4. 9-4 Area of Composite Figures
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

5. 9-4 Area of Composite Figures
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.

6. 9-4 Area of Composite Figures
Additional Example 1A Continued
Find the shaded area. Round to the nearest
tenth, if necessary.
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

7. 9-4 Area of Composite Figures
Additional Example 1B: Finding the Area of
Composite Figures by Adding
Find the shaded area. Round to the nearest
tenth, if necessary.
A = bh
A = 20 • 8
A = 160 in2
12 in.
area of the rectangle:
20 in.
8 in.
Divide the figure into a rectangle
and a semicircle.
8 in.8 in.

8. 9-4 Area of Composite Figures
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
Find the shaded area. Round to the nearest
tenth, if necessary.
12 in.
20 in.
8 in.
8 in.
Add the area of the rectangle and the area of the
semicircle.
total area: A = 160 + 25.1 = 185.1 in2
.

9. 9-4 Area of Composite Figures
A = bh
A = 8 • 9
A = 72 yd2
area of the rectangle:
Check It Out! Example 1A
Find the shaded area. Round to the nearest
tenth, if necessary.
Divide the figure into a rectangle
and a triangle.
10 yd
9 yd
8 yd

10. 9-4 Area of Composite Figures
Check It Out! Example 1A Continued
Find the shaded area. Round to the nearest
tenth, if necessary.
area of the triangle:
A = bh
1
2
__
A = (2 • 9)
1
2
__
A = (18)
1
2
__
A = 9 yd2
Add the area of the rectangle and the area of the
triangle.
total area: A = 72 + 9 = 81 yd2
10 yd
9 yd
8 yd

11. 9-4 Area of Composite Figures
Check It Out! Example 1B
Find the shaded area. Round to the nearest
tenth, if necessary.
A = bh
A = 22 • 10
A = 220 m2
12 m
area of the rectangle:
22 m
Divide the figure into a rectangle
and a semicircle.
10 m
10 m

12. 9-4 Area of Composite Figures
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
Find the shaded area. Round to the nearest
tenth, if necessary.
Add the area of the rectangle and the area of the
semicircle.
total area: A = 220 + 39.3 = 259.3 m2
12 m
22 m
10 m
10 m

13. 9-4 Area of Composite Figures
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

14. 9-4 Area of Composite Figures
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.

15. 9-4 Area of Composite Figures
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

16. 9-4 Area of Composite Figures
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

17. 9-4 Area of Composite Figures
Additional Example 3 Continued
What is the area of the room
floor shown in the figure?
Round to the nearest tenth.
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:

18. 9-4 Area of Composite Figures
Check It Out! Example 3
What is the area of the stage
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.
5 ft
5 ft
10 ft10 ft
15 ft

19. 9-4 Area of Composite Figures
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

20. 9-4 Area of Composite Figures
Check It Out! Example 3 Continued
What is the area of the room
floor shown in the figure?
Round to the nearest tenth.
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:

21. 9-4 Area of Composite Figures
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems

22. 9-4 Area of Composite Figures
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

23. 9-4 Area of Composite Figures
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

24. 9-4 Area of Composite Figures
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