Question

Find the area of an equilateral triangle having altitude h cm.

Answer 1

Altitude of an equilateral triangle = h

Let side of an equilateral triangle = x

$\therefore h=\frac{\sqrt{3}}{2}x\Rightarrow x=\frac{2\times h}{\sqrt{3}}=\frac{2h}{\sqrt{3}}$

Now area= $\frac{\sqrt{3}}{4}\times sid{e}^2$

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

= $\frac{h^2}{\sqrt{3}}c{m}^2$