To calculate the moment of inertia for a structure made of three identical thin rods, each of length L and mass M, the appropriate formulas are Icm = 1/12 ML^2 and I = 1/3 ML^2. The moment of inertia for Rod C, which is aligned with the axis of rotation, is determined to be 1/3 ML^2. For Rod A, the moment of inertia must consider the varying distances of its particles from the axis. The Parallel Axis Theorem is necessary for calculating the moment of inertia for Rod B. The discussion concludes with the participant confirming their understanding of the calculations.