Given plate has mass M and area $3a^2$

A square plate of side $2a$ (made of the same material) has mass $\frac{4M}{3}$ and

Therefore moment of inertia about its axis is

$I_1=\frac{1}{6}\left(\frac{4M}{3}\right){\left(2a\right)}^2$

A square plate of side $a$ (made of the same material) has mass $\frac{M}{3}$ and

Therefore moment of inertia about its axis is $I_2=\frac{1}{6}\left(\frac{M}{3}\right)a^2$

Moment of inertia of the given plate is

$I=I_1-I_2=\frac{5}{6}M{a}^2$