9.1.3 Composite Figures Key Objectives • Use the Area Addition Postulate to find the areas of composite figures. • Use composite figures to estimate the areas of irregular shapes. Key Terms • A composite figure is made up of simple shapes, such as triangles, rectangles, trapezoids, and circles. Example 1 Finding the Areas of Composite Figures by Adding
The area of a composite figure is determined by addition in this example. The figure is a rectangle topped by a triangle. The length and width of the rectangle is given. The lengths of the three sides of the triangle are given. Substitute the known values for the length and width into the formula for the area of a rectangle, A = lw . The area of the rectangle is 80 cm 2 . The formula for the area of a triangle is A bh The line forming the height of the triangle bisects the width of the rectangle and forms two smaller right triangles with one leg 4 cm and hypotenuse 5 long. The second leg, the height, is 3 cm, because this is a Pythagorean triple. Substituting the height and base length into the formula for area gives 12 cm 2 . The sum of the two areas is 92 cm 2 . 1 2 . = The area of a composite figure is determined by addition in this example. The figure consists of a rectangle, right triangle, and semicircle. The width of the rectangle and the lengths of the legs of the triangle are given. Because this is a right triangle, the base and height lengths are equal to the two legs of the triangle. Substituting the height and base lengths into the formula for area of a triangle gives 49/2 in 2 . The length of the hypotenuse of the triangle is equal to the length of the rectangle. The triangle is a 45°-45°-90° triangle with legs 7 in., so the hypotenuse is equal to 7 2 in. The area of the rectangle is 28 2 in 2 . The semicircle diameter is equal to the length of the rectangle. Substituting this value into the formula for one-half the area of a circle gives the area of the semicircle as 49 π /4 in 2 . The sum of the three areas, determined using a calculator, is 102.6 in 2 .
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