The sum of the areas of the parallelogram polyominoes having semi-perimeter n+2 is equal to 4 n . In this paper we give a simple proof of this property by means of a mapping from the cells of parallelogram polyominoes having semi-perimeter n+2 to the 4 n words of length n of the free monoid {a,b,c,d} ∗ . This mapping works in linear time. Then, we introduce a tiling game arising from this enumerative property.