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The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism?

The base of a prism is in the shape of an equilateral triangle. If the perimeter of the base is 18 cm and the height of the prism is 20 cm, then what is the volume (in cm3) of the prism? Correct Answer 180√3

Perimeter of base (equilateral triangle) = 3 × side = 18cm

⇒ Side of base = 6 cm

⇒ Area of base = side2 × (√3/4)

⇒ Area of base = (√3/4) × 6 × 6

⇒ Area of base = 9√3cm

⇒ Volume of prism (V) = area of base × height

∴ Volume of prism (V) = 9√3 × 20 = 180√3 cm3

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