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4/20/2015 9-3 C Area of Composite Figures

• To find the area of ANY composite figure, separate it into figures that you know how to solve for

Example 1Find the area of the figure.

Area of Rectangle Area of Triangle

A = bh

A = 10 ● 15 or 150

The height of the triangle is 14 – 10 or 4 centimeters.

The area is 150 + 10 or 160 square centimeters.

Example 2The diagram shows the dimensions of a window. Find the area of the window. Round to the nearest tenth.

The figure can be separated into a semicircle and a rectangle.

The height of the rectangle is 7.2 – 1.7, or 5.5 feet.

The area of the rectangle is 3.4 × 5.5 or 18.7 square feet.

The area of the window is 4.5 + 18.7 or about 23.2 square feet.

2 or about

Example 3Find the area of the figure.

The figure can be separated into two rectangles. The shared square, however, will be counted twice if the areas are added, so the area ofthe small square, 1 × 1, or 1 square meter, must be subtracted from the total.The area of the top rectangle is 5 × 2 or 10 square meters.The area of the bottom rectangle is 2 × 6 or 12 square meters.The sum of the areas is 10 + 12 or 22 square meters.

So, the area of the figure is 21 square meters.

Example 4

Find the area of the polygon.

1.7 cm

4.9 cm 1.3 cm

2.1 cm

A = lw A = lw

A = 4.9 • 1.7 A = 2.1 • 1.3

A = 8.33 A = 2.73

8.33 + 2.73 = 11.06

The area of the polygon is 11.06 cm2.

1.7 cm

4.9 cm

1.3 cm

2.1 cm

Example 5

Find the area of the polygon.

A = lw

A = 28 • 24

A = 672 A = 168

672 + 168 = 840

The area of the polygon is 840 ft2.

A = bh12__

A = • 28 • 1212__

Example 6

Patrick made a design. Use the coordinate grid to find its area.

Rectangle 1

l = 5, w = 5; A = 5 • 5 = 25

Rectangle 2l = 10, w = 5; A = 10 • 5 = 50

Rectangle 3l = 15, w = 5; A = 15 • 5 = 75

Rectangle 4l = 20, w = 5; A = 20 • 5 = 100

0

10

15

20

5 10

5

15 20 25

25

25 + 50 + 75 + 100 = 250 square units.

The area of the design is 250 square units.

1. Find the area of the figure shown.

220 units2

2. Phillip designed a countertop. Use the coordinate grid to find its area.

30 units2

Exit Ticket

1. Find the area of the figure.

A. 27 units2 B. 54 units2

C. 93 units2 D. 98 units2

Homework

• Pg. 563 #1-20 Evens• Study for Chapter 9 Test