A study was conducted to investigate the critical points of oriented area regarded as a function on the moduli space of a polygonal linkage. Jacob Steiner showed that the area of a polygon with fixed edge lengths attained its maximum at the cyclic polygon. Physically, a polygonal linkage was interpreted as a set of cyclically joined rigid rods of length l _i. Free bending and self-intersections, along with self-overlaps of edges were allowed at the locations of joints. Theorem 1 stated that the set of A critical points coincided with the set of all cyclic configurations for any generic polygonal linkage. This theorem was proved by Steiner's four-hinge method, which consisted in fixing n - 2 vertices of the configuration and considering the bendings generated by the quadrangular linkage.