Question

The base of a prism is an equilateral triangle of perimeter 15 cm and the height is 5 cm. What is the volume of the prism?

• A. $\frac{125\sqrt{3}}{4}c{m}^3$
  
• B. $\frac{75\sqrt{3}}{4}c{m}^3$
  
• C. $\frac{85\sqrt{3}}{4}c{m}^3$
  
• D. $\frac{175\sqrt{3}}{4}c{m}^3$

Answer 1

The correct option is A

$\frac{125\sqrt{3}}{4}c{m}^3$

Perimeter of the equilateral triangle is 15 cm

Hence each side of the equilateral triangle = $\frac{15}{3}=5cm$

Area of the triangular base = $\frac{\sqrt{3}}{4}\times (5{)}^2=\frac{25\sqrt{3}}{4}c{m}^2$

Volume of prism = $\text{Base Area}\times \text{Height}=\frac{25\sqrt{3}}{4}5$

$=\frac{125\sqrt{3}}{4}c{m}^3$