A metallic sheet of mass m has the shape of a square of side length l. Then moment of inertia of the sheet about axis PQ is 

The axes PQ and RS are mutually perpendicular. Then by perpendicular axis theorem, 

${\mathrm{I}}_{\mathrm{PQ}}+{\mathrm{I}}_{\mathrm{RS}}={\mathrm{I}}_{\mathrm{x}}+{\mathrm{I}}_{\mathrm{y}}={\mathrm{I}}_{\mathrm{z}}$

from symmetry, ${\mathrm{I}}_{\mathrm{PQ}}={\mathrm{I}}_{\mathrm{RS}}\mathrm{and}{\mathrm{I}}_{\mathrm{x}}={\mathrm{I}}_{\mathrm{y}}$

$\therefore 2{\mathrm{I}}_{\mathrm{PQ}}=2{\mathrm{I}}_{\mathrm{x}}={\mathrm{I}}_{\mathrm{z}}\Rightarrow {\mathrm{I}}_{\mathrm{PQ}}={\mathrm{I}}_{\mathrm{x}}=\frac{1}{2}{\mathrm{I}}_{\mathrm{z}}=\frac{1}{12}{\mathrm{ml}}^2$