Question

Find the volume of a quilateral triangle based prism if the perimeter of the base is $6$cm and height is $18$cm.

Answer 1

The perimeter of the base is $P=3s$, since it is a triangle, therefore,

$6=3\times s$

$s=2$

Now, the area of the base $B=\frac{\sqrt{3}}{4}{s}^2$ with $s=2$ cm is:

$B=\frac{\sqrt{3}}{4}{s}^2=\frac{\sqrt{3}}{4}\times 2\times 2=\sqrt{3}$ cm${}^2$

The general formula for volume of prism is $V=Bh$ where $B$ is the area of the base and $h$ is the height.

Since area of the base is $B=\sqrt{3}$ cm${}^2$ and the height $h=18$ cm, therefore, the volume is:

$V=Bh=\sqrt{3}\times 18=18\sqrt{3}$ cm${}^3$

Hence, the volume of the prism is $18\sqrt{3}$ cm${}^3$.