To find the centre of gravity using geometrical methods.
Make a hole near the edge of the cardboard, and hang it on a nail. Make a plumb line by tying a weight to a piece of string. Hang the thread on the nail and mark the vertical line with a pencil. The centre of gravity always seeks the lowest position it can attain hence it is somewhere on this vertical line. Make another hole at some other spot near the cardboard's edge and repeat the same procedure. The spot where the two lines cross is the centre of gravity. The centre of gravity of a piece of cardboard is the spot where it will balance on a pointed object.