Q$\mathrm{.}2)($a$)$ Find the centroid $(\stackrel{}{x}\frac{,}{b}ar(y))$ of the composite area shown below.

$($b$)$ Determine the area moment of inertia $(x^{\text{'}}$ and $I_{y^{\text{'}}})$ of the composite area about its centroidal axes found in part $($a$).$