A built$-$up section similar to that shown in Figure $7$ in the text consists of a $24\frac{3}{8}$ web plate, four $64\frac{1}{2}$ angles placed with their long legs outstanding,

and two $14\frac{1}{2}$ cover plates. The area of a $64\frac{1}{2}$ angle is $4\mathrm{.}75$ sq in$.,$ the moment of inertia of an angle with respect to the axis through its centroid that is

parallel to the longer leg is $6\mathrm{.}3$ in$.{?}^4,$ and the distance from the back of the longer leg to the centroid is $0\mathrm{.}99$ in$.$ If the distance between the backs of the angles is

$24\frac{1}{2}$ in$.,$ what is the moment of inertia of the entire section with respect to the neutral axis that is perpendicular to the web plate, as axis XX in Figure $7?($Shown

above$)$

A$.4900$ in$.4$

B$.4777$ in ${?}^4$

C$.5029$ in$.4$

D$.5054$ in$.{?}^4$