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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 1 Find the area of the figure.

The area is 150 + 10 or 160 square centimeters. Area of Rectangle Area of Triangle The height of the triangle is 14 – 10 or 4 centimeters. A = bh A = 10 ● 15 or 150 The area is 150 + 10 or 160 square centimeters.

Example 2 The 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.

2 or about 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.

Example 3 So, the area of the figure is 21 square meters. Find 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 of the 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

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.

Example 5 Find the area of the polygon.

A = bh 1 2 __ A = lw A = • 28 • 12 1 2 __ A = 28 • 24 A = 168 A = 672 672 + 168 = 840 The area of the polygon is 840 ft2.

Patrick made a design. Use the coordinate grid to find its area. Example 6 Patrick made a design. Use the coordinate grid to find its area. Rectangle 1 l = 5, w = 5; A = 5 • 5 = 25 25 20 Rectangle 2 15 l = 10, w = 5; A = 10 • 5 = 50 10 Rectangle 3 5 l = 15, w = 5; A = 15 • 5 = 75 5 10 15 20 25 Rectangle 4 l = 20, w = 5; A = 20 • 5 = 100

25 + 50 + 75 + 100 = 250 square units. The area of the design is 250 square units.

Exit Ticket 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

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