For the composite shape shown to the right:

a$)$ Determine the centroid with respect to the given coordinate system.

b$)$ Compute the moment of inertia about the given $y-$axis, $I_y.$

$80$

$I_x=\frac{1}{12}b{h}^3$

$I_y=\frac{1}{12}h{b}^3$

$I_{x^{\text{'}}}=\frac{1}{36}b{h}^3$

$I_{y^{\text{'}}}=\frac{1}{36}h{b}^3$