Four L$3\backslash (\backslash$times $3\backslash$times $\backslash$frac$\{1\}\{4\}\backslash )-$in$.$ angles are welded to a rolled W section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal $\backslash ($ x $\backslash )$ and $\backslash ($ y $\backslash )$ axes if $\backslash ($ a$=6\backslash )$ in$.$

The moment of inertia with respect to the $\backslash ($ x $\backslash )$ axis is in $\backslash (\{\}^\{4\}\backslash ).$

The radius of gyration with respect to the $\backslash ($ x $\backslash )$ axis is

The moment of inertia with respect to the $\backslash ($ y $\backslash )$ axis is in$.$ The radius of gyration with respect to the $\backslash ($ y $\backslash )$ axis is in $4.$

in$.$