A hollow square has inner dimensions a x a and outer dimensions 2a x 2a. Find moment of inertia about the outer side.

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$I_{A B}=\left[I_{G}+A h^{2}\right]_{1}-\left[I_{G}+A h^{2}\right]_{2}$

$I_{A B}=\left[\frac{b^{4}}{12}+A h^{2}\right]_{1}-\left[\frac{b^{4}}{12}+A h^{2}\right]_{2}$

$I_{A B}=\left[\frac{(2 a)^{4}}{12}+(2 a \times 2 a) \times a^{2}\right]_{1}-\left[\frac{(a)^{4}}{12}+(a \times a) \times a^{2}\right]_{2}$

$I_{A B}=\left[\frac{16 a^{4}}{12}+4 a^{4}\right]_{1}-\left[\frac{a^{4}}{12}+a^{4}\right]_{2}$

$I_{A B}=\left[\frac{64 a^{4}}{12}\right]_{1}-\left[\frac{13 a^{4}}{12}\right]_{2}$

$I_{A B}=a^{4}\left[\frac{64-13}{12}\right]$

$I_{A B}=a^{4}\left[\frac{51}{12}\right]$

$I_{A B}=4.25 a^{4}$

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