Area of the shaded region in the figure below is?

\(\frac{a^2}{2}\) (\(\pi \) - 2)

Area of shaded region is -

Ar. of semicircle - area of ΔABC

ΔABC is isosceles triangle

since AC = AB =  \(\sqrt {2}\)a

altitude of ΔABC = a

Base = 2a = diameter

area = \(\frac{1}{2}\) Base × alt = \(\frac{1}{2}\) × a × 2a = a²

Area of semicircle = \(\frac{1}{2}\)πa²

Area of shaded region = \(\frac{1}{2}\)πa² - a²

                                 = (\(\frac{π - 2}{2}\)) a²

                                 = \(\frac{a^2}{2}\) (π - 2)