Holt CA Course 1 9-5 Area of Composite Figures Warm Up Warm Up Lesson Presentation Lesson...

Holt CA Course 1

9-5 Area of Composite Figures

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Holt CA Course 1


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.

40 cm2

216 ft2

64 cm2

78.5 in2

Holt CA Course 1


MG2.2 Estimate and compute the area of more complex or irregular two-and three-dimensional figures by breaking the figures down into more basic geometric objects.

California Standards

Holt CA Course 1

9-5 Area of Composite FiguresAdditional 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

8 m

8 m

area of the rectangle:

2 m

6 m

Divide the figure into a rectangle and a trapezoid.

2 m

6 m

12 m

4 m

Holt CA Course 1

9-5 Area of Composite FiguresAdditional Example 1A Continued


8 m

area of the trapezoid:

2 m

6 m

2 m

6 m

A = h(b1 + b2)12

__

A = 2(4 + 2)12

__

A = (12) 12

__

A = 6 m2 Add the area of the rectangle and the area of the trapezoid.total area: A = 72 + 6 = 78 m2.

4 m

Holt CA Course 1

9-5 Area of Composite FiguresAdditional Example 1B: Finding the Area of

Composite Figures by Adding


A = bh

A = 20 • 8

A = 160 in2

12 in.


20 in.

8 in.

Divide the figure into a rectangle and a semicircle.

8 in.8 in.

Holt CA Course 1


area of the semicircle:

A = (r2)12__

A (3.14 • 42)12

__

A (50.24) 12

__

A 25.1 in2

Additional Example 1B Continued


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.

Holt CA Course 1


A = bh

A = 8 • 9

A = 72 yd2


Check It Out! Example 1A


Divide the figure into a rectangle and a triangle.

10 yd

9 yd

8 yd

Holt CA Course 1

9-5 Area of Composite FiguresCheck It Out! Example 1A Continued

Find the shaded area. Round to the nearest tenth, if necessary. area of the triangle:

A = bh12__

A = (2 • 9)12

__

A = (18) 12

__

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

Holt CA Course 1


Check It Out! Example 1B


A = bh

A = 22 • 10

A = 220 m2

12 m


22 m

Divide the figure into a rectangle and a semicircle.

10 m

10 m

Holt CA Course 1


area of the semicircle:

A = (r2)12__

A (3.14 • 52)12

__

A (78.5) 12

__

A 39.3 m2

Check It Out! Example 1B Continued


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

Holt CA Course 1

9-5 Area of Composite FiguresAdditional Example 2: Finding the Area of Composite

Figures by SubtractingFind the shaded area.

A = bh

A = 12 • 9 = 108 ft2

Area of the rectangle:

Area of the triangle:

A = bh12

__

A = • (6)(7)12__

A = • 42 = 21 ft212

__Shaded area:

Subtract the area of the triangle from the area of the rectangle.

A = 108 – 21 = 87 ft2

5 ft

12 ft

6 ft9 ft

Holt CA Course 1

9-5 Area of Composite FiguresCheck It Out! Example 2

Find the shaded area.

A = bh

A = 16 • 8 = 128 in2


Area of the triangle:

A = bh12

__

A = • (5)(7)12__

A = • 35 = 17.5 in212

__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.

Holt CA Course 1


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

Holt CA Course 1

9-5 Area of Composite FiguresAdditional 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


A = r212__

A • 3.14 • (9)212

__

A (254.34)

127.17 ft2

12

__

Area of the semicircle:

18 ft

Holt CA Course 1


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:

Holt CA Course 1


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

Holt CA Course 1

9-5 Area of Composite FiguresCheck 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


A = r212__

A • 3.14 • (7.52)12

__

A (314)

88.3 ft2

12

__

Area of the semicircle:

15 ft

Holt CA Course 1


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:

Holt CA Course 1

9-5 Area of Composite FiguresLesson Quiz: Part l

Find the perimeter and area of each figure. Round to the nearest tenth, if necessary.

1.

2.

111 ft2

188.9 mm2

5 ft3.

45.9 in2

Holt CA Course 1


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

Holt CA Course 1 9-5 Area of Composite Figures Warm Up Warm Up Lesson Presentation Lesson...

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