Elementary Geometry for College Students (5th Edition)

Published by Brooks Cole
ISBN 10: 1439047901
ISBN 13: 978-1-43904-790-3

Chapter 8 - Section 8.2 - Perimeter and Area of Polygons - Exercises - Page 372: 30

Answer

A$\approx$119.43

Work Step by Step

Since the two base angles of triangle VRS have a measure of 60 degrees, it must be an equilateral triangle. In this case all of the sides are equal to 8$\sqrt 2$. The height of this triangle would be 4$\sqrt 6$. Since sides RW, VW, TS, and VT are all congruent, triangles RWV and STV are congruent isosceles right triangles with hypotenuses equal to 8$\sqrt 2$. Therefore these four congruent sides are equal to 8. A=2(.5)(8$^2$)+.5(4$\sqrt 6$)(8$2$) A=64+16$\sqrt 12$ A$\approx$119.43
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