Consider the cross$-$section with dimensions as provided below, and complete the following. Use $a=4^{\text{'}\text{'}},b={0\mathrm{.}5}^{\text{'}\text{'}},$ and $c=3^{\text{'}\text{'}}.$

a$.$ Calculate the cross$-$sectional area of the cross$-$section,

b$.$ Determine the distance $\frac{?}{\text{b}\text{a}\text{r}}(y)$ to the centroid of the beam's cross$-$sectional area;

c$.$ Find the moment of inertia about the centroidal $x^{\text{'}}$ axis.

d$.$ Determine the moment of inertia about the $y$ axis.