Why is moment of inertia r=3 and not half the diagonal?

[Hanin]

Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the rectangle).

 

[RedDelicious]

Review your definitions. r is the perpendicular distance from the mass to the axis of rotation, which is that entire line through the center, not the distance from the mass to the point in the center.

 

[rude man]

I think you were thinking rotation about the c.g. into/out of page.