In the first part, we introduce the class of vertex convexity polygons, and we show that all 4-gons belong to this class. We define a point in some polygons, and in the second part, we prove that in a 4-gon this is the center of gravity. We calculate this barycenter by a subdivision of the polygon into two triangles. Then we compute the barycenters of the triangles. The barycenter of the 4-gon results in the barycenter of the two barycenters of the triangles with taking into account the areas of the triangles.
