The base of a prism is an equilateral triangle of perimeter 15 centimetres square and its height is 5 centimetres. Calculate its volume.

Given: base of prism is equilateral triangle and perimeter of base “p” = 15cm²

Height of prism “h” = 5cm

To find : Volume “V” of the prism = ?

Procedure :

As we know that, base of prism is equilateral triangle and its perimeter is 3× side of triangle

⇒ p = 3× side

⇒ 15 = 3× side

∴ side of the triangular base of the prism = = 5cm

Now, area of the equilateral triangular base of the prism,

“a” = × side²

= ×5²

= ×25

⇒ a = 10.83cm²

As we know that, Volume of the prism = height × area of base

∴ V = h × a

= 5 × 10.83

= 54.15cm³

∴ Volume of the given prism is 54.15cm³.