Derive an expression for perpendicular axis theorem?

Question: Derive an expression for perpendicular axis theorem?

The perpendicular axis theorem states that the moment of inertia of a planar body about an axis perpendicular to the plane of the body is equal to the sum of the moments of inertia of the body about any two perpendicular axes intersecting at the first axis. Mathematically, if I_x, I_y, and I_z are the moments of inertia of the body about three mutually perpendicular axes x, y, and z, then the moment of inertia I_z about the z-axis is given by I_z = I_x + I_y. This theorem is useful for finding the moment of inertia of a complex shape by dividing it into simpler shapes and summing their moments of inertia.

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