Correct Answer: $144\sqrt3\text{ cm}^2$

Solution : Given: The length of the median of an equilateral triangle is $12\sqrt3\text{ cm}$.
The height of an equilateral triangle of the side $x$ is $\frac{\sqrt3}{2} x$ and its area is given as $\frac{\sqrt3}{4} x^2$.
According to the question,
$\frac{\sqrt3}{2} x =12\sqrt3 $
⇒ $x=24\text{ cm}$
Then, the area of the triangle is given as,
$\frac{\sqrt3}{4}\times x^2$
$=\frac{\sqrt3}{4}\times (24)^2$
$=144\sqrt3\text{ cm}^2$
Hence, the correct answer is $144\sqrt3\text{ cm}^2$.