Moment of inertia for a rectangular lamina about the axis in the plane of lamina passing through the end and parallel to the breadth is
Axis is in the plane of the lamina passing through the end & parallel to the breadth.
The mass distribution of lamina in the above case is like a rod for which axis pass through its end hence the moment of inertia for a rectangular lamina about the axis in the plane of lamina passing through the end and parallel to the breadth is