Question

A circle is inscribed in an equilateral triangle. If the inradius is $21cm$. what is the area of the triangle?

Answer 1

Height of the equilateral triangle = 3 x 21 = 63 cm
$\frac{\sqrt{3}}{2}\times side=63cm$
$\Rightarrow$ Side $=\frac{63\times 2}{\sqrt{3}}cm$
Area of the triangle $=\frac{\sqrt{3}}{4}\times S^2$
$=\frac{\sqrt{3}}{4}\times \frac{63\times 2}{\sqrt{3}}\times \frac{63\times 2}{\sqrt{3}}$
$=1323\sqrt{3}$ sq units