We first find the area of polygons resulting from the transformation of the boundary of any given convex polygon by moving its vertices in a prescribed way. This area is determined in terms of the given polygon characteristics. We show that it is not possible to express the new polygon area as a simple multiple of the first polygon area if this one has more than four sides. The above transformation is then iterated and the areas of the corresponding polygons are determined. The last section is devoted to the same study for plane convex regions with a smooth boundary. We obtain a general formula giving the area of any n-iterated transformation of such a region.

iterated transformations of convex polygons or regions, area of transformed convex regions.