Determine the moment of interia of the distribution of parti

Determine the moment of interia of the distribution of particles in the figure bellow respect an axis that pass through the particles 2 and 8.

Solution

moment of inertia = m1r1^2 + ......

as 2,8 lies on axis so I2=I8 = 0

now all other masses are at equal distance from this axis = sqrt3*a/2

=> I = 6*m*(sqrt3*a/2)^2 = 4.5ma^2

where a is length of one side