Recently the problem of finding the mass, centre of gravity and moments of inertia for laminae bounded by polygons arose in a programming course for first year civil engineering degree students. It was suggested that it would be useful for them to construct a program that would take as input the vertices of the polygon, and print out area, centroid and moment of inertia. In order to make the program have a logically simple structure, the method presented in this note was devised. After consultation with many standard textbooks and engineering handbooks it was discovered that the method was either original or completely neglected. Since in many respects the method compares favourably with the subdivision techniques of the standard sources it would appear to be worth publicising the technique.