In the sequence of diagrams that follow, regular polygons are inscribed in unit circles with at least one side of each polygon perpendicular to the x-axis. Prove that the perimeter of each polygon in the sequence is given by an=2nsin(/n), where n is the number of sides in the polygon. Solution suppose polygon has n sides each side makes angle 2(p/n) at center each side length=r*sin(p/n)+r*sin(p/n)=2r*sin(p/n) sum of n sides=2*n*r*sin(p/n).