Find the moment of inertia of a uniform square plate of mass `M` and edge a about one of its diagonals.

Explanation

To find the moment of inertia of a uniform square plate of mass \( M \) and edge \( a \) about one of its diagonals, we can follow these steps:

### Step 1: Understand the Geometry
We have a uniform square plate with mass \( M \) and edge length \( a \). The square plate has two diagonals, and we need to find the moment of inertia about one of these diagonals.

### Step 2: Moment of Inertia about an Axis Perpendicular to the Plate
The moment of inertia of a square plate about an axis perpendicular to the plate and passing through its center is given by the formula:
\[
...