A triangle with all side lengths rational is said to be a rational triangle. It is known - for example, Cutting the unit square into pieces with rational length sides - that the unit square allows partition into triangles all of which are rational. It follows from the above-linked discussion that any rectangle with length and width rational (diagonal whatever) can be cut into rational rectangles by a recursive application of the unit square method (thanks to Peter Taylor for clarifying this point I had overlooked in an earlier post).
Question: for a general polygon P to be divisible into some finite number of rational triangles, it is obviously necessary that all sides of P are rational in length. What could one say about sufficiency conditions? As a special case, how could one characterize a quadrilateral that can be cut into some finite number of rational triangles?
