False. Although a square and a circle can have the same area, their moments of inertia are different because the moment of inertia depends on the shape of the object in relation to its axis of rotation.
The moment of inertia (I) is calculated using the formula I = ∫r² dm, where r is the distance from the axis of rotation to the mass element dm. For a circle, the formula for moment of inertia about an axis through its center is I = (π/4) r^4 (where r is the radius), and for a square, the moment of inertia about an axis through its center is I = (1/6) a^4 (where a is the side length).
Even though both shapes can be designed to have the same area, their dimensions differ which affects their moment of inertia. This is why the statement is false; shape plays a crucial role in determining the moment of inertia regardless of area.