The height of an equilateral triangle is $5\sqrt{3}\, cm$, then its area is:

$25\sqrt{3}\, cm^2$

The correct answer is Option (4) → $25\sqrt{3}\, cm^2$

The given height is $5\sqrt{3}$​ cm.

For an equilateral triangle:

$h = \frac{\sqrt{3}}{2}a$

So,

$a = \frac{2h}{\sqrt{3}} = \frac{2 \times 5\sqrt{3}}{\sqrt{3}} = 10 \text{ cm}$

Now, area:

$\text{Area} = \frac{\sqrt{3}}{4}a^2 = \frac{\sqrt{3}}{4} \times 100 = 25\sqrt{3}\ \text{cm}^2$