The given shape's centroid is located at point C$.$ It has an area of $1200$ in ${?}^2$ and a moment of inertia about its centroidal $x^{\text{'}}$ and $y^{\text{'}}$ axis of $90,000$ in $4$ and $160,000$ in ${?}^4$ respectively.

The distances $d_x$ and $d_y$ are equal to $10$ in and $15$ in respectively. What is the moment of inertia about the $y$ axis?

$280,000$ in ${?}^4$

$430,000$ in ${?}^4$

$360,000i{n}^4$

$210,000i{n}^4$