Question

A triangular prism has an equilateral triangular base. The side of the triangle is 8 cm and the height of the prism is 14 cm. What is the volume of the triangular prism?

• A. $204\sqrt{3}c{m}^3$
• B. $234\sqrt{3}c{m}^3$
• C. $214\sqrt{3}c{m}^3$
• D. $224\sqrt{3}c{m}^3$

Answer 1

The correct option is D

$224\sqrt{3}c{m}^3$

Let 's' be the side of the triangle, here s=8 cm . height h = 14 cm

$Areaofbase=A=\frac{\sqrt{3}}{4}\times s^2$

$\Rightarrow A=\frac{\sqrt{3}}{4}\times 8^2$

$\Rightarrow A=\frac{\sqrt{3}}{4}\times 64$

$\Rightarrow A=\sqrt{3}\times 16$

$\Rightarrow A=16\sqrt{3}c{m}^2$

$Volume=A\times h=16\sqrt{3}\times 14=224\sqrt{3}c{m}^3$