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 use the Perpendicular Axis Theorem. Here’s the step-by-step solution:

### Step 1: Understand the Geometry
We have a uniform square plate with mass \( M \) and side length \( a \). The diagonals of the square intersect at the center of the square and are perpendicular to each other.

### Step 2: Identify the Axes
We will denote:
- \( I_1 \): Moment of inertia about one diagonal.
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