Question

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

• A. $425\sqrt{3}c{m}^3$
• B. $415\sqrt{3}c{m}^3$
• C. $435\sqrt{3}c{m}^3$
• D. $525\sqrt{3}c{m}^3$

Answer 1

The correct option is A

$425\sqrt{3}c{m}^3$

Perimeter = 30 cm

$Sideofthetriangle=\frac{perimeter}{3}=\frac{30}{3}=10cm$

Height h =17 cm

$Areaofbase\left(A\right)=\frac{\sqrt{3}}{4}\times s^2$

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

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

$=\sqrt{3}\times 25$

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

$Volume=A\times h=25\sqrt{3}\times 17=425\sqrt{3}c{m}^3$