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(D) The altitude $h$ of an equilateral triangle with side length $a$ is given by the formula $h = \frac{\sqrt{3}}{2} a$.Given $h = 12 \sqrt{3} 	ext{

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$144 \sqrt{3} 	ext{ cm}^2$

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(D) The altitude $h$ of an equilateral triangle with side length $a$ is given by the formula $h = \frac{\sqrt{3}}{2} a$.Given $h = 12 \sqrt{3} 	ext{ cm}$,we have $\frac{\sqrt{3}}{2} a = 12 \sqrt{3}$.By canceling $\sqrt{3}$ from both sides,we get $\frac{a}{2} = 12$,which implies $a = 24 	ext{ cm}$.The area $A$ of an equilateral triangle is given by $A = \frac{\sqrt{3}}{4} a^2$.Substituting $a = 24$,we get $A = \frac{\sqrt{3}}{4} 	imes (24)^2 = \frac{\sqrt{3}}{4} 	imes 576$.$A = 144 \sqrt{3} 	ext{ cm}^2$.

If the altitude of an equilateral triangle is $12 \sqrt{3} \text{ cm}$,then its area would be

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