9.1.3 Composite Figures (continued) Example 2 Finding the Areas of Composite Figures by Subtracting
The area of a composite figure is determined by subtraction in this example. The figure is a triangle with a square removed. The length of a side of the square, the height of the triangle above the square, and the length of a side of the triangle are given. The height of the triangle is the height of the square plus the height above the square, or 5 m. The right triangle formed by the height line is a 5, 12, 13 Pythagorean triple, so the length of the base of the large triangle is 24 m. Substitute the known values for the base and height into the formula for the area of a triangle. The area of the triangle is 60 m 2 . The area of the square is the length of the side squared, or 9 m 2 . The area of the triangle minus the area of the square is 51 m 2 . The area of a composite figure is determined here by subtraction. The figure is a square with a semicircle and two quarter circles removed. The side of the square is given. The area of the square is the length of the side squared, or 100 ft 2 . The semicircle and the two quarter circles combine to form a complete circle. The diameter of the circle is equal to the length of a side of the square. Substitute one-half the length of the diameter into the formula for the area of a circle. The area of the circle is 25 π ft 2 . The area of the square minus the circle is 100 − 25 π ≈ 21.5 ft 2 .
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