Question

The total surface area of a triangular based prism is $576c{m}^2$ and its height is $22$cm. If the area of its base is $24c{m}^2$, find the perimeter of its base.

Answer 1

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 the total surface area is $TSA=576$ cm${}^2$ and the base is $B=24$ cm and height is $h=22$ cm, therefore, the perimeter of its base is:

$TSA=Ph+2B\Rightarrow 576=22P+(2\times 24)\Rightarrow 576=22P+48\Rightarrow 22P=576-48\Rightarrow 22P=528\Rightarrow P=\frac{528}{22}=24$

Hence, perimeter of its base is $24$ cm.