Question

Find the area of an equilateral triangle whose height is $\frac{\sqrt{3}}{2}$ cm.

Answer 1

Given the height of the equilateral triangle is $\frac{\sqrt{3}}{2}$ cm.

Let $a$ be the side of the triangle.

Then we have,

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

or, $a=1$.

Then area of the triangle will be $\frac{\sqrt{3}}{4}\times a^2$

Area $=\frac{\sqrt{3}}{4}$ cm${}^2$. [ Since $a=1$]