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: 17

Answer

The area of the shaded region: 57 cm$^{2}$

Work Step by Step

To find the area of the shaded region simply find the area of the semicircle and subtract the area of the triangle. Area of a Semicircle: $A$$_{semi}$ = $\pi$$r$$^{2}$ / 2 Therefore: $A$$_{semi}$ = (3.14)(10 cm)$^{2}$ / 2 $A$$_{semi}$ = 157 cm$^{2}$ $A$$_{tri}$ = $\frac{1}{2}$$b$$h$ $A$$_{tri}$ = $\frac{1}{2}$(20 cm)(10 cm) $A$$_{tri}$ = 100 cm$^{2}$ $A$$_{total}$ = $A$$_{semi}$ - $A$$_{tri}$ $A$$_{total}$ = 157 cm$^{2}$ - 100 cm$^{2}$ $A$$_{total}$ = 57 cm$^{2}$
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