The area of the shaded region in the figure given below is

Area of shaded region = Area of semicircle - Area of triangle
$$\eqalign{ & = \frac{{\pi {{\left( a \right)}^2}}}{2} - \frac{1}{2} \times a \times 2a \cr & = \frac{{\pi {a^2}}}{2} - {a^2} \cr & = {a^2}\left( {\frac{\pi }{2} - 1} \right){\text{ sq}}{\text{. units}} \cr} $$