Question

In the given figure, the shaded area is

• A. $a^2(\frac{4\pi }{3}-\sqrt{3})$
• B. $a^2(4\pi -\sqrt{3})$
• C. $a^2(2\pi -\frac{\sqrt{3}}{2})$
• D. None

Answer 1

The correct option is A $a^2(\frac{4\pi }{3}-\sqrt{3})$

ABC is equilateral $\Delta$ with side 2a.
$\frac{AO}{OD}=\frac{2}{1}\Rightarrow AO=\frac{2}{3}AD=\frac{2}{3}\times \sqrt{3}$
$\pi (AO{)}^2-\frac{\sqrt{3}}{4}\times (2a{)}^2=a^2(\frac{4\pi }{3}-\sqrt{3})$