The base of a right prism is an equilateral t | vedclass

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(D) The area of the base of an equilateral triangle is given by the formula: $	ext{Area} = \frac{\sqrt{3}}{4} 	imes 	ext{side}^2$. Substituting the

Vedclass · Accepted Answer

$12$

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(D) The area of the base of an equilateral triangle is given by the formula: $	ext{Area} = \frac{\sqrt{3}}{4} 	imes 	ext{side}^2$. Substituting the given side length of $6 \, cm$: $	ext{Area} = \frac{\sqrt{3}}{4} 	imes 6^2 = \frac{\sqrt{3}}{4} 	imes 36 = 9 \sqrt{3} \, cm^2$. The volume of a right prism is calculated as: $	ext{Volume} = 	ext{Area of base} 	imes 	ext{height}$. Given the volume is $108 \sqrt{3} \, cm^3$,we have: $108 \sqrt{3} = 9 \sqrt{3} 	imes h$. Dividing both sides by $9 \sqrt{3}$: $h = \frac{108 \sqrt{3}}{9 \sqrt{3}} = 12 \, cm$.

The base of a right prism is an equilateral triangle with a side of $6 \, cm$. If the volume of the prism is $108 \sqrt{3} \, cm^3$,its height is ...... $cm$.

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