Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its center and is parallel to two of its sides. CD is a linen in the plane of the plate and it passes through the center of the plate, making an angle \(\theta\) with AB. The moment of inertia of the plate about the axis CD is equal to : 

\(I\)

I_AB = I_A'B' = I and I_CD = I_C'D' 

if I_o is moment of inertia of square plate about axis passing through o and perpendicular to plane then by perpendicular axis theorem,

I_o = I_AB + I_A'B' = 2I_AB ... (i) or       

I_o = I_CD + I_C'D' = 2I_CD  ... (ii)

(i) & (ii) gives :

I_AB = I_CD = I