The answers are:
The volume: 12387.44 cm3
The lateral surface area: 2400 cm²
The volume (V) of pentagonal prism is:
\(V= \frac{1}{4} \sqrt{5(5+2 \sqrt{5}) } *a ^{2} *h\)
where:
a is the side of the base,
h is the altitude (height) of the prism.
It is given:
a = 15 cm
h = 32 cm
Thus:
\(V= \frac{1}{4} \sqrt{5(5+2 \sqrt{5}) } *15 ^{2} *32\)
V = 12387.44 cm³
The lateral surface area (A1) of the pentagonal prism is:
A1 = 5 a h
A1 = 5 15 32 = 2400 cm²
