Problem $12$ For the shaded area below, find the location of the centroid with respect to the bottom of the shape. Then, find the moment of inertia of the composite area about that centroid. The following formulas are provided for your use:

$\stackrel{}{x}=\frac{{\displaystyle \underset{?}{\overset{?}{}}}{x}_i{A}_i}{{\displaystyle \underset{?}{\overset{?}{}}}{A}_i}\frac{,}{b}ar(y)=\frac{{\displaystyle \underset{?}{\overset{?}{}}}{y}_i{A}_i}{{\displaystyle \underset{?}{\overset{?}{}}}{A}_i},I_{\text{r}\text{e}\text{c}\text{t},\text{c}\text{e}\text{n}\text{t}}=\frac{b{h}^3}{12}$ and $I^{\text{'}}=I_c+A{d}^2$