Farmers Field

Age 11 to 14 Challenge Level:

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are expensive to build, so naturally the farmer wishes to build the shortest wall he can.

Can you prove that the shortest wall is always straight, whatever the shape of the original field? Or perhaps you can find a shape where the shortest wall isn't straight!