\[\begin{array}{*{35}{l}}

y~=\text{ }\surd \left( {{a}^{2}}~-~{{x}^{2}} \right)\text{ }\Rightarrow ~{{y}^{2}}~=~{{a}^{2}}~-~{{x}^{2}}  \\

{{x}^{2~}}+~{{y}^{2}}~=~{{a}^{2}}  \\

\end{array}\]

which is equation of a circle.

the area of the shaded region is

Therefore, the required area = πa²/4