(Solved): The moments of inertia of the rectangle and right-angled triangle with respect to the given system ...

The moments of inertia of the rectangle and right-angled triangle with respect to the given system of axes are indicated in the sketches. Point $C$ denotes in each case the centroid of the region. $\begin{array}{l}\text{ Area }=12{\mathrm{m}}^2\\ I_x=9{\mathrm{m}}^4\\ I_y=16{\mathrm{m}}^4\end{array}$ $\begin{array}{l}\text{ Area }=2.88{\mathrm{m}}^2\\ I_x=I_y=0.9216{\mathrm{m}}^4\end{array}$ Find the moment of inertia $I_x$ of the composite region below. $I_x=m^4$