Question

A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the volume of the prism is 81, what are the lengths of the sides of the base?

Answer 1

Lengths of the sides (there are 3 sides in an equilateral triangle) of the base of prism is 5.72cm each.

Explanation:

As the base of triangular prism is equilateral:

∴ Area of base = (√ 3 / 4)× (side)²

According to question:

height of prism = height (side) of base

Volume of prism = 81 cm³,

∴ Volume of prism = Area of base x height

⇒ 81 cm³ = (√ 3 / 4)× (side)² × height ∵ side = height

⇒ 81 cm³ = (√ 3 / 4)× (side)³

⇒ 81 × (4/√3) cm³ = side³

⇒ ∛(81 × (4/√3) cm = side

⇒ side = 5.72cm