Elementary Geometry for College Students (5th Edition)

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

Chapter 11 - Test: 20

Answer

$A=5a^2tan(36)$

Work Step by Step

We draw an apothem. Then, we draw a triangle that extends to a corner of the pentagon closest to the apothem. This means the angle created is: $360/10=36$ We will call the apothem a. If we call the side that runs along the side of the pentagon b, we can find: $tan(36)=b/a$ This means $b=atan(36)$ From this, we find that the area of the triangle is: $A=.5bh=.5a(atan(36))$ $A=.5a^2tan(36)$ Since there are 10 of these triangles within the pentagon, the total area is: $A=5a^2tan(36)$
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