Elementary Geometry for College Students (7th Edition)

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 9 - Section 9.2 - Pyramids, Area, and Volume - Exercises - Page 417: 23a


$144.9$ cm$^2$

Work Step by Step

The base of this pyramid is a pentagon, therefore we can split the base into 5 equal triangles. We can now split any of these triangles into two from the center of the pentagon to the center of the base, into two right triangles. We can now apply the area of a triangle $\frac{bh}{2}$ , double it, and multiply by 5. Base of the right triangle. (Half of the length of one of the pentagon's sides.): $b=4.6cm$ Apothem: $h=9.2/2=6.3cm$ $\frac{(4.6)(6.3)}{2}*2*5$ =$144.9$ cm$^2$
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