Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 10 - Area - Chapter Review - Page 680: 46

Answer

$18.29 \ cm^2$

Work Step by Step

Our aim is to compute the area of a circle. Let $A$ be the area of a circle. $A=\pi r^2$ Plug the given data in the above equation to obtain: $A=3.14 (8)^2=200.96 \ cm^2$ In order to get the arc length $l$, we need to multiply the area of a circle by $\dfrac{90^{\circ}}{360^{\circ}}$. So, we have: $A=\dfrac{90^{\circ}}{360^{\circ}} \times 200.96 =50.24 \ cm^2$ The area of a triangle is equal to: $A=\dfrac{1}{2}(8)(8) \sin 90^{\circ}=32 \ cm^2$ Thus, the area of a shaded region is:$A=50.24 -32=18.29 \ cm^2$
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