The decomposition of planar polygons into triangles is a well studied area of Computer Graphics with particular relevance to GIS. Trapezoidation is often performed as a first step to triangulation. Though a linear time algorithm [2] for the decomposition of a simple polygon into triangles exists, it is extremely complicated and in practice O(n log n) algorithms are used. We present a very simple O (n) -time heuristics for the trapezoidation of simple polygons without holes. Such polygons commonly occur in Geographic Information Systems (GIS) databases.