Question

In the given figure, a circular arc of radius $6cm$ has been drawn with vertex O of an equilateral $△OAB$ of side $12cm$ as the center.

The area of the shaded region is,

• A. $156.522c{m}^2$
• B. $156.552c{m}^2$
• C. $165.552c{m}^2$
• D. $561.552c{m}^2$

Answer 1

Answer: (B)

$156.552c{m}^2$

Area of shaded region $=$ Area of circle + Area of $\Delta OAB$ - Area of sector $A^{\prime }O{B}^{\prime }$

$=\pi r^2+\frac{\sqrt{3}}{4}(side{)}^2-\frac{{60}^o}{{360}^o}\times \pi (6{)}^2$

$=\pi (6{)}^2+\frac{\sqrt{3}}{4}(12{)}^2-6\pi$

$=36\pi +\frac{\sqrt{3}}{4}\left(144\right)-6\pi$

$=94.2+62.352$

$=156.552c{m}^2$

Hence option ${}^{\prime }{B}^{\prime }$ is the answer.