Area of a POLYGON

From figure we can observe that all the side that having in polygon are equal length . so if we add all the vertex from the center than we will get all the triangle having same area . Now the angle created from the center is ((2*pi)/n) , as total angle from center is 2*pi. so for 1 triangle the area is

(1/2)*a*b*sin((2*pi)/*n).
here a=b=r;
so area of 1 triangle = 
(1/2)*(r*r*sin((2*pi)/n))
so for the n triangles the total area is 

area of polygon

n * (1/2)*(r*r*sin((2*pi)/n))
observe the figure more for  detail

so now solve this problem 
UVA 10432 (area of polygon)