Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 8 - Review Exercises - Page 386: 35

Answer

$9\pi - 18$

Work Step by Step

We know that the triangle only coincides in half of the circle. Thus, the area of the circle around the triangle is: $A = \pi(6^2) \times 1/2 = 18\pi$ We know that, since the triangle forms a 45-45-90 triangle when cut in two, each side is $6\sqrt2$. This means that the area is: $A = 1/2(6\sqrt2)(6\sqrt2) = 36$ Thus, the area of both regions is: $A = 18\pi-36 $ This means that the area of one region is: $9\pi - 18$
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