PROBLEM $9\mathrm{.}37$

Determine the shaded area and its moment of inertia with respect to the centroidal axis parallel to $A{A}^{\text{'}},$ knowing that its moments of inertia with respect to $A{A}^{\text{'}}$ and $B{B}^{\text{'}}$ are $2000$ in$^4$ and $4000$ in$^4$ respectively, and that $d_1=8in.$ and $d_2=4in.$