Question

In the figure, a circle inscribed in an equilateral triangle $ABC$ of side $12cm$. Find the radius of the inscribed circle and the area of the shaded region. [Use $\pi =3.14$ and $\sqrt{3}=1.73$]

Answer 1

$\frac{r}{6}=\tan {30}^o=\frac{1}{\sqrt{3}}$

$\therefore r=2\sqrt{3}$

Area of $△=\frac{\sqrt{3}}{4}\times {12}^2=36\sqrt{3}$

$=36\times 1.73$

$=62.28$

Area of circle $=\pi r^2$

$=3.14\times 12$

$=37.18$

Shaded $=24.6c{m}^2$