An equilateral triangular lamina ABC of mass M has moment of inertia I₀ about an axis through its centroid perpendicular to its plane. D, E, F are the mid-points of the sides and the medial triangle DEF is cut out. The moment of inertia of the remaining part about the same axis is

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(1) (15)/(16)I₀. DEF is similar with half the side, so its area is 1/4 (mass /M4) and, sharing the same centroid, its MI scales as the square of its mass-times-size: I_DEF=(1/4)(1/2)² I₀=1/(16)I₀. Iᵣₑₘ=I₀-1/(16)I₀=(15)/(16)I₀.

An equilateral triangular lamina ABC of mass M has moment of inertia I₀ about an axis through its centroid perpendicular to its plane. D, E, F are the mid-points of the sides and the medial triangle DEF is cut out. The moment of inertia of the remaining part about the same axis is

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