Question

The base of a right prism is an equilateral triangle with a side 6 cm and its height is 18 cm. Find its volume, lateral surface area and total surface area ?

Answer 1

Volume of a right prism = Area of base × height. 

Since the base is an equilateral triangle of side 6 cm, 

Area of base = \(\frac{\sqrt3}{4}\) x (side)² = \(\bigg(\frac{\sqrt3}{4}\times6^2\bigg)\)cm² = \(\frac{\sqrt3}{4}\) x 36 cm² = \(9\sqrt3\) cm²

∴ Volume = (\(9\sqrt3\) x18) cm³ = 162√3 cm³ 

Lateral surface area = Perimeter of the base × Height 

= (6 + 6 + 6) cm × 18 cm = 18 cm × 18 cm = 324 cm² 

Total surface area = Lateral surface area + Area of ends (bases) 

= (324 + 2 × 9√3 ) cm² = (324 + 18√3 ) cm² = (324 + 31.176) cm² = 355.176 cm².