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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