#### Answer

468 $in.^{2}$

#### Work Step by Step

Lateral area = perimeter $\times$ h
Lateral area = (9 in. + 15 in. + 12 in.) $\times$ 10 in.
Lateral area = 360 $in.^{2}$
Base area = $\sqrt (s (s-a)(s-b)(s-c) )$
s= $\frac{9 in. + 15 in. + 12 in.}{2}$ = 18 in.
a=9 in.
b=15 in.
c=12 in.
Base area = 54 $in.^{2}$
Total area = 2 $\times$ base area + lateral area
Total area = 2 $\times$54 $in.^{2}$ + 360 $in.^{2}$
Total area = 468 $in.^{2}$