Basic College Mathematics (9th Edition)

Published by Pearson
ISBN 10: 0321825535
ISBN 13: 978-0-32182-553-7

Chapter 8 - Geometry - 8.6 Circles - 8.6 Exercises: 18

Answer

The area of the shaded region is $\approx 232.8$ in$^{2}$.

Work Step by Step

1. Find area of the semicircle Let $S =$ area of the semicircle (Note: Radius $= diameter \div 2 = 18 \div 2= 9$ in.) $S = \frac{1}{2}\pi r^{2}$ $S = \frac{1}{2}(3.14)(9^{2})$ $S = 254.34 \times 0.5$ $S = 127.17$ in$^{2}$ 2. Find the rectangle Let $R =$ area of the rectangle $R = length \times width$ $R = 20 \times 18$ $R = 360$ in$^{2}$ 3. Find the area of the shaded region by subtracting the area of the rectangle from the area of the semicircle Let $A =$ area of the shaded region $A = R - S$ $A = 360 - 127.17$ $A = 232.83$ in$^{2}$ $A \approx 232.8$ in$^{2}$
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