The base of a right prism is an equilateral triangle. The lateral surface area of prism is 252 sq. cm and the volume of the prism is 147√3 cm². Then, what is the side (in cm) of the base of the prism?

Question

Question

Answer 1

Given:

Lateral surface area of prism is 252 sq. cm

Volume of the prism is 147√3 cm²

Formula used:

Lateral surface area of prism = perimeter of base × height

Volume of the prism = Area of base × height

Calculation:

F1 Mohd.S 30-05-2020 Savita D8

Let the side of the base of prism be a cm and height of the prism be h cm.

Lateral surface area of prism = perimeter of base × height

⇒ Lateral Surface Area of Prism = 3 × a × h = 252

⇒ ah = 252/3

⇒ ah = 84 ---- (1)

The volume of the prism = Area of base × height

\(\Rightarrow 147\sqrt 3 = \frac{{\sqrt 3 }}{4} \times {\left( a \right)^2} \times h\;\)

\(\Rightarrow 147\sqrt 3 = \frac{{\sqrt 3 }}{4} \times a \times ah\)

\(\Rightarrow 147\sqrt 3 = \frac{{\sqrt 3 }}{4} \times a \times 84\;\)

⇒ 147 = 21 × a

⇒ a = 7 cm

∴, the side of the base of the prism is 7 cm.