Question : The median of an equilateral triangle is $6\sqrt3$ cm. The area (in cm2) of the triangle is:
Option 1: $72$
Option 2: $108$
Option 3: $72\sqrt3$
Option 4: $36\sqrt3$
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Correct Answer: $36\sqrt3$
Solution : Given: Median = AD = $6\sqrt3$ cm Let AB = BC = CA = $a$ cm So, $\frac{\sqrt3}{2}a$ = $6\sqrt3$ ⇒ $a$ = $12$ cm Now, the area of $\triangle$ABC = $\frac{\sqrt3}{4}×a^2$ = $\frac{\sqrt3}{4}×12×12$ = $36\sqrt3$ cm 2 Hence, the correct answer is $36\sqrt3$.
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