Question

Find the area of the shaded region in fig, where is circular arc of radius $6cm$ has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side $12cm$ as centre

Answer 1

Area of Shaded region $=$ Area of equilateral triangle $ABO$ $+$ Area of Major sector
Area of Equilateral Triangle ABO $=\frac{\sqrt{3}}{4}\times a^2$ $=\frac{\sqrt{3}}{4}\times 12\times 12c{m}^2$

$=62.352c{m}^2$
Area of major sector $=\frac{\theta }{360}\times \pi \times r^2$

$=\frac{300}{360}\times \pi \times 6\times 6c{m}^2$
$=94.2c{m}^2$
Area of Shaded region $=$ $62.352+94.2$ $=156.55c{m}^2$