The area of the shaded region in the adjoining figure is

A. $${a^2}\left( {\pi - 1} \right)sq.units$$

B. $${a^2}\left( {\frac{\pi }{2} - 1} \right)sq.units$$

C. $$\frac{{{a^2}}}{2}\left( {\pi - 1} \right)sq.units$$

D. $$\frac{{{a^2}}}{2}\left( {\frac{\pi }{2} - 1} \right)sq.units$$

Answer: Option B

Solution(By Examveda Team)

Area of the shaded region = Area of the semi-circle with radius a units $$-$$ Area of the triangle with base 2a units and height a units
$$\eqalign{ & = \left( {\frac{{\pi {a^2}}}{2} - \frac{1}{2} \times 2a \times a} \right)sq.units \cr & = \left( {\frac{{\pi {a^2}}}{2} - {a^2}} \right)sq.units \cr & = {a^2}\left( {\frac{\pi }{2} - 1} \right)sq.units \cr} $$