9-4 Area of Composite Figures

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Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

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.

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.

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

9-4 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

area of the rectangle:

Divide the figure into a rectangle and a trapezoid.

9-4 Area of Composite FiguresAdditional Example 1 Continued

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

8 marea 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

9-4 Area of Composite Figures

Check It Out: Example 1

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

9-4 Area of Composite Figures

Check It Out: Example 1 Continued

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

Area of rectangle: 9 × 8 = 72 yd

Area of triangle: (2)(9) = 9 yd

Area of composite figure: 72 + 9 = 81 yd

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2

2

2

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 = 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

9-4 Area of Composite Figures

Check It Out: Example 2

Find the shaded area.9 in.

16 in.

5 in.8 in.

area of rectangle: A = lw = 16 8 = 128

area of triangle: A = bh = (5 7) = (35) = 17.5

area of shaded area: A = 128 - 17.5 = 110.5 in2

2 2_1

211

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

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 = r212__

A • 3.14 • (9)212

__

A (254.34)

127.17 ft2

12

__

Area of the semicircle:

18 ft

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:

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.

9-4 Area of Composite Figures

Check It Out: Example 3 Continued

area of top rectangle: A = lw = 5 · 5 = 25area of large rectangle: A = lw = 15 · 5 = 75

area of semicircle: A = r ≈ (3.14 · 7.5 )

≈ (176.6) = 88.3total area: A = 25 + 75 + 88.3 = 188.3 ft

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9-4 Area of Composite Figures

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

9-4 Area of Composite Figures

Lesson Quiz: Part lFind the shaded area of each figure. Round to the nearest tenth, if necessary.

1.

2.

111 ft2

188.9 mm2

5 ft3.

45.9 in2

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

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