The height of an equilateral triangle is 6 cm. Its area is

(a) $12 \sqrt{3} \mathrm{~cm}^{2}$

Height of equilateral triangle $=\frac{\sqrt{3}}{2} \times$ Side

$\Rightarrow 6=\frac{\sqrt{3}}{2} \times$ Side

$\Rightarrow$ Side $=\frac{12}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=\frac{12}{3} \times \sqrt{3}=4 \sqrt{3} \mathrm{~cm}$

Now,

Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$

$=\frac{\sqrt{3}}{4} \times(4 \sqrt{3})^{2}$

$=\frac{\sqrt{3}}{4} \times 48$

$=12 \sqrt{3} \mathrm{~cm}^{2}$