Question

The perimeter of the base of an equilateral triangular prism is 30 cm. The height of the prism is 17 cm. Find the volume of the prism.

Answer 1

Given:
Perimeter = 30 cm
Height = 17 cm

The base is an equilateral triangle.
$\therefore \text{Length of a side of the triangle}=\frac{Perimeter}{3}=\frac{30}{3}=10cm$

$\text{Area of the base}=\frac{\sqrt{3}}{4}\times {\text{Length of a side}}^2$

$=\frac{\sqrt{3}}{4}\times {10}^2$

$=\frac{\sqrt{3}}{4}\times 100$

$=\sqrt{3}\times 25$

$=25\sqrt{3}c{m}^2$

$\text{Volume of the prism}=Areaofthebase\times Height=25\sqrt{3}\times 17=425\sqrt{3}c{m}^3$