MK-MO 1996 Problem 2

Let $P$ be the set of all polygons in the plane and let $M : P \to R$ be a mapping that satisfies: (i) $M(P) \ge 0$ for each polygon $P$ , (ii) $M(P) = x^2$ if $P$ is an equilateral triangle of side $x$ , (iii) If a polygon $P$ is partitioned into polygons $S$ and $T$ , then $M(P) = M(S)+ M(T)$ , (iv) If polygons $P$ and $T$ are congruent, then $M(P) = M(T )$ . Determine $M(P)$ if $P$ is a rectangle with edges $x$ and $y$ .