PROBLEM $9\mathrm{.}56$

A channel and an angle are welded to an $\backslash ($ a $\backslash$times $20-\backslash$mathrm$\{$mm$\}\backslash )$ steel plate. Knowing that the centroidal $\backslash ($ y $\backslash )$ axis is located as shown, determine $($a$)$ the width $\backslash ($ a $\backslash ),($b$)$ the moments of inertia with respect to the centroidal $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ axes.