Question

The side of a square based prism is $2.5$cm and its height is $6.5$cm. Find its lateral and total surface area.

Answer 1

The perimeter $P$ of the prism is $P=4\times side$, therefore, the perimeter of prism with side $2.5$ cm is $P=4\times 2.5=10$ cm.

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 prism is $P=10$ cm and the height is $h=6.5$ cm, therefore, the lateral surface area is:

$LSA=P\times h=10\times 6.5=65$ cm${}^2$

The general formula for the total surface area of a right prism is $TSA=Ph+2B$ where $P$ represents the perimeter of the base, $h$ is the height of the prism and $B$ is the area of the base.

Since $LSA=Ph=65$ cm${}^2$ and the base is $B=2.5$ cm, therefore, the total surface area is:

$TSA=2(2.5{)}^2+65=12.5+65=77.5$cm${}^2$

Hence, lateral surface area is $65$cm${}^2$ and total surface area is $77.5$cm${}^2$.