Question

The Base of a prism is a regular pentagon with one side measuring 15cm. Find the volume and the lateral surface area if the altitude measures 32cm.

Answer 1

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