Question

In an equilateral triangle of side $24cm$, a circle is inscribed touching its sides. Find the area of the remaining portion of the triangle.

Answer 1

We have $R=\frac{A}{s}$

$A=$Area of triangle

$s=$ Semi perimeter

$R=$ Radius of incircle

$s=\frac{24\times 3}{2}=36cm$

$A=\left(\sqrt{3}/4\right){24}^2=144\sqrt{3}c{m}^2$

$R=\frac{144\sqrt{3}}{36}=4\sqrt{3}cm$

Area of in circle$=\pi R^2=\pi \times 4^2\times 3=48\pi c{m}^2$

Area of remainig portion$=(144\sqrt{3}-48\pi )c{m}^2$