The area of the shaded region in the adjoining figure is

Answer: Option B

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
$$\begin{array}{rl}& =\left(\frac{\pi a^2}{2}-\frac{1}{2}\times 2a\times a\right)sq.units\\ & =\left(\frac{\pi a^2}{2}-a^2\right)sq.units\\ & =a^2\left(\frac{\pi }{2}-1\right)sq.units\end{array}$$