#### 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:
$V = 19.7~in^3+19.7~in^3 = 39.4~in^3$