$(20$pts$)$ The following are field notes for an irregular cross section. Compute the cross$-$sectional area using coordinate method. The roadway is $24$ ft wide and side slopes are $1$:$2.$

$\backslash$table$[[\frac{c5\mathrm{.}20}{13\mathrm{.}3},\frac{c4\mathrm{.}87}{7\mathrm{.}73},\frac{c2\mathrm{.}33}{2\mathrm{.}80},\frac{c3\mathrm{.}73}{0},\frac{c4\mathrm{.}87}{13\mathrm{.}28}$