Question

The shape of a pole is in the form of a square based prism. If its side is $2$ feet and lateral surface area is $160$ square feet, find the height of the pole.

Answer 1

The perimeter $P$ of the prism is $P=4\times side$, therefore, the perimeter of prism with side $2$ ft is $P=4\times 2=8$ ft.

The general formula for the lateral surface area of a right prism is $LSA=Ph$ where $P$ represents the perimeter of the base and $h$ represents the height of the prism.

Since the perimeter of the pole is $P=8$ ft and the lateral surface area is $LSA=160$ ft${}^2$, therefore, the height of the pole is:

$LSA=P\times h\Rightarrow 160=8\times h\Rightarrow h=\frac{160}{8}=20$

Hence, the height of the pole is $20$ feet.