Theorem of Perpendicular Axes
According to this theorem, the sum of moment of inertia of a plane lamina about two mutually perpendicular axes lying in its plane is equal to its moment of inertia about an axis perpendicular to the plane of lamina and passing through the point of intersection of first two axes (Fig. 3).
Iz = Ix + Iy
Note: In case of symmetrical two-dimensional bodies, as moment of inertia for all axes passing through the center of mass and in the plane of body will be same, so the two axes in the plane of body need not be perpendicular to each other.