Question $7$ : $(15$ Points$)$

In the cross section shown :

a$-$ Find the centroid of the shaded area.

b $-$ Find the Moment of Inertia with respect to the x and y axes shown.

Answers:

$\stackrel{}{x}=0,$widetilde$(y)=5\mathrm{.}87in$

$I_x=1,738\mathrm{.}3i{n}^4,I_y=134\mathrm{.}8i{n}^4$