Moment of inertia of a square plate of mass M of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by (approx)

For a rectangular sheet, moment of inertia passing through O and perpendicular to its plane is
${\mathrm{I}}_0=\mathrm{M}\left(\frac{{\mathrm{l}}^2+{\mathrm{b}}^2}{12}\right)$ Now, for a square plate, ${\mathrm{I}}_0=\frac{{\mathrm{Ml}}^2}{6}\text{ and }\mathrm{r}=\sqrt{\frac{{\mathrm{l}}^2}{4}+\frac{{\mathrm{l}}^2}{4}}=\frac{\mathrm{l}}{\sqrt{2}}$
Moment of inertia about B parallel to the axis through O is I=I₀+Mr²
$=\frac{{\mathrm{Ml}}^2}{6}+\frac{{\mathrm{Ml}}^2}{2}=\frac{2}{3}{\mathrm{Ml}}^2$