Question

The height of an equilateral triangle is $\sqrt{6}$ cm. Its area is

(a) 3$\sqrt{3}$ cm² (b) 2$\sqrt{3}$ cm² (c) 2$\sqrt{2}$ cm² (d) 6$\sqrt{2}$ cm²

Answer 1

Let a and h respectively be the side and height of the equilateral triangle.
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{a^2\sqrt{3}}{4} \\ \Rightarrow \frac{a^2\sqrt{3}}{4}=\frac{1}{2}\times a\times h \\ \Rightarrow \frac{a\sqrt{3}}{4}=\frac{1}{2}\times \sqrt{6} \\ \Rightarrow a=2\sqrt{2} \end{gathered}$$
Therefore
$\mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{{\left(2\sqrt{2}\right)}^2\sqrt{3}}{4}=2\sqrt{3}{\mathrm{cm}}^2$
Hence, the correct option is (b).