$5\mathrm{.}20$ and $5\mathrm{.}21$ The horizontal $\backslash ($ x $\backslash )$ axis is drawn through the centroid $\backslash ($ C $\backslash )$ of the area shown, and it divides the area into two component areas $\backslash ($ A$\_\{1\}\backslash )$ and $\backslash ($ A$\_\{2\}\backslash ).$ Determine the first moment of each component area with respect to the $\backslash ($ x $\backslash )$ axis, and explain the results obtained.

Note: Do both $5\mathrm{.}20$ and $5\mathrm{.}21$ and please show diagrams and clear steps. Thank you.

Fig. P$5\mathrm{.}21$