Cut a rectangular piece of heavy cardboard into two pieces with different shapes that you think have the same area.

One way to determine if the areas are roughly the same is to compare the weights of the two pieces. Assuming that the thickness of the cardboard is constant, if the weights are the same, then the areas must be the same.

You can compare weights by taping each piece to one end of a string, marking the midpoint of the string, then placing a pencil under the midpoint, as shown in the following diagram. If the string does not move, the pieces balance.