How to find moment of inertia of equilateral triangle?

Below are few steps which are helpful to find the moment of inertia of an equilateral triangle

with the system of particles about an axis passing through the center of mass of the system and perpendicular to the plane containing them.

- Let the measure of the side of the equilateral triangle be ‘a’.
- The distance ‘r’ from any vertex of the equilateral triangle to the centre of mass can be found using the formula
- The formula for moment of inertia is
- If there are 3 particles of mass ‘m’ placed at each of the vertex of this equilateral triangle then we consider three times m.