The base of a right prism is an equilateral triangle with a side 6 cm

1.	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» 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.

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»

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.