Question

If volume of an equilateral triangle based prism is $72\sqrt{3}{m}^3$ and height is $7$m, find the length of the base.

Answer 1

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

Since volume of the prism is $V=72\sqrt{3}$ m${}^2$ and the height $h=7$ m, therefore, the area of base is:

$V=Bh\Rightarrow 72\sqrt{3}=7B\Rightarrow B=\frac{72\sqrt{3}}{7}$

Now, the area of the base $B=\frac{\sqrt{3}}{4}{s}^2$, therefore,

$B=\frac{\sqrt{3}}{2}{s}^2\Rightarrow \frac{72\sqrt{3}}{7}=\frac{\sqrt{3}}{2}{s}^2\Rightarrow s^2=\frac{72\times 2}{7}=\frac{144}{7}\Rightarrow s=\sqrt{\frac{144}{7}}=\frac{12}{\sqrt{7}}$

Hence, the length of the base is $\frac{12}{\sqrt{7}}$ m.