Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 9 - Section 9.2 - Pyramids, Area, and Volume - Exercises - Page 409: 45

Answer

$V = 39.4~in^3$

Work Step by Step

Since the hexagonal pyramid has plane symmetry with respect to a plane determined by apex $G$ and the vertices $A$ and $D$, the pyramid with base $ABCD$ and apex $G$ has the same volume as the pyramid with base $ADEF$ and apex $G$. Therefore, both of these pyramids have a volume of $19.7~in^3$ The volume of the given hexagonal pyramid is the sum of these two smaller pyramids. We can find the total volume: $V = 19.7~in^3+19.7~in^3 = 39.4~in^3$
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