If the height of an equilateral triangle is $12\sqrt{3}$ cm, then its area is :

1. $44\sqrt{3}$ cm²

2. $144\sqrt{3}$ cm²

3. $140\sqrt{3}$ cm²

4. $132\sqrt{3}$ cm²

Let the length of each side of the equilateral triangle be a cm.

We know that,

Height of an equilateral triangle = $\dfrac{\sqrt{3}}{2}$ side

⇒ $12\sqrt{3} = \dfrac{\sqrt{3}}{2}a$

⇒ a = 24 cm.

$\Rightarrow \text{Area of an equilateral triangle} = \dfrac{\sqrt{3}}{4} \times a^2 \\[1em] = \dfrac{\sqrt{3}}{4} \times (24)^2 \\[1em] = \dfrac{\sqrt{3}}{4} \times 24 \times 24 \\[1em] = \sqrt{3} \times 24 \times 6 \\[1em] = 144 \sqrt{3} \text{ cm}^2.$

Hence, option 2 is the correct option.