#2015_14 From an old Physics Olympiad!

Consider a long solid, rigid hexagonal prism like a common type of pencil. The mass of the prism is \(M\) and is uniformly distributed. The length of each side of cross-sectional hexagon is \(a\). The moment of inertia \(I\) of the hexagonal prism about its central axis is \[I=\frac { 5 }{ 12 } M{ a }^{ 2 } \] Find the moment of inertia \(I\) of the hexagonal prism about an edge of the prism.

Details and Assumptions:

  • \(M=1 \text{ kg}\), \(a=1 m\)
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