Fundamental Problem $10\mathrm{.}8$

Take that $\backslash ($ a$=30\backslash$mathrm$\{$~mm$\}\backslash )$ and $\backslash ($ b$=120\backslash$mathrm$\{$~mm$\}\backslash )$

Determine the moment of inertia of the cross$-$sectional area of the $\backslash ($ T $\backslash )-$beam with respect to the $\backslash ($ x$^\{\backslash$prime$\}\backslash )$ axis passing through the centroid of the cross section. $($Figure $1)$ Express your answer to three significant figures and include the appropriate units.

Answer is not $5\mathrm{.}206$e$7$ mm$4$

Figure