How to find the center of mass of a square

If we draw the diagonals to the square, than the point where the two diagonals intersect gives you the geometric centre for that square which is also called as the centre of mass for a uniform square shaped lamina.

Also note that the centre of mass need not be at the geometric centre if the square has uneven mass distribution, and in such case the centre of mass will shift towards the region where there is higher mass.