Question

The area of the shaded region in the adjoining figure if every circle is of unit radius is

• A. $(\sqrt{3}-\frac{\pi }{2})sq.units$
• B. $(\sqrt{3}+\pi )sq.units$
• C. $(2\sqrt{3}-\frac{\pi }{2})sq.units$
• D. $(\sqrt{3}-\frac{\pi }{4})sq.units$

Answer 1

The correct option is A $(\sqrt{3}-\frac{\pi }{2})sq.units$

Area of sector =$\frac{\theta }{360}\times \pi r=\frac{60}{360}\times \pi (1{)}^2=\frac{\pi }{6}$

Then area of 3 sectors =$\frac{\pi }{6}\times 3=\frac{\pi }{2}$

And area of triangle =$\frac{\sqrt{3}}{4}(2{)}^2=\frac{\sqrt{3}}{4}\times 4=\sqrt{3}$

Then area of shaded portion =

$\sqrt{3}-\frac{\pi }{6}unit$