ABCD is a square plate with centre O. The moments of inertia of the plate about the axis perpendicular to the plane and passing through O is I and about the axes 1,2,3 &4 are $I_1,I_2,I_3,I_4$  respectively. It follows that :

Momentum of inertia of the plate about An axis passing through the centre O and perpendicular to the plane is 

$I_0=I_1+I_2=I_3+I_4$ ------- (1) 

$I_1=I_2=I$ and  $I_3=I_4=I^1$

$I_0=2I=2I^1$-------- (2) 

For square plate,  $I=\frac{M{L}^2}{12}$

$I_0=2\left(\frac{M{L}^2}{12}\right)=\frac{M{L}^2}{6}$

From (1)

$I_1+I_2=I_3+I_4=\frac{M{L}^2}{6}$

$I=I^1=\frac{M{L}^2}{12}$ from (2)

$\Rightarrow I_1=I_2=I_3=I_4=\frac{M{L}^2}{12}$

$I_0=I_1+I_4\Rightarrow I_0=I_2+I_4$