a$)(15$ pts$)$ Locate the centroid $(\stackrel{}{x}\frac{,}{b}ar(y))$ of the shaded area.

b$)(20$ pts$)$ Calculate the moment of inertia of the shaded area about each centroidal axes $(\frac{?}{\text{b}\text{a}\text{r}}(I{)}_x\frac{,}{b}ar(I{)}_y).$ Use parallel$-$axis theorem: $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_x\frac{?}{b}=ar(I{)}_{x^{\text{'}}}+A(y{)}^2$ and $\frac{?}{\text{b}\text{a}\text{r}}(I{)}_y\frac{?}{b}=ar(I{)}_{y^{\text{'}}}+A(x{)}^2.$