Suppose that the owner of a circular field of unit radius (with irrational area p)wishes to rearrange arcs of the field’s fence to instead enclose a rational area. The curvature of the arcs cannot be changed and the fence should remain connected. The owner loves geometry and wants the shape of the new fence to also be geometrically constructible, that is, able to be drawn using only a straightedge and compass. Are there any rational areas that the owner can enclose? And if so, how should the fence be divided and what shapes will the fence enclose?