How can we show that the area of a regular polygon of n sides circumscribe circle of radius r is:

http://3.bp.blogspot.com/-6cdMKOSZHXg/TiVuzvEZDqI/AAAAAAAAABs/wCWJeD9hfz4/s1600/given.JPG

Your formula is incorrect. Note that nr^2\tan(\frac {180} 2) \ = \ \infty. Perhaps you meant this:


A = nr^2 \tan(\frac {180^{\small o}} n)


A regular polygon is made up of a bunch of triangles, and the area of each triangle is 1/2 base times height. Draw a diagram and determine how the base length and height of each traingle relates to the radius of the circle and the number of triangles of the polygon.