A theorem is proposed for the areas of n-sided convex polygons, of given lengths of sides. The theorem is illustrated as a simple but powerful one in estimating the areas of irregular polygons, being dependent only on the number of sides n (and not on any of the specific angles) of the irregular polygon. Finally, because of the global symmetry shown by equilateral triangles, squares and circles under group (gauge) theory, the relationships govering this areas, when their are inscribed or escribed in one another are discussed as riders, and some areas of their applications in graph theory, ratios and maxima and minima problems of differential calculus briefly mentioned