# Area of a polygon

• Mar 22nd 2007, 01:26 PM
Recklessid
Area of a polygon
Hello, I was wondering if anyone can help me with this problem.
A) Let A_n be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle of (2pi)/n, show that A_n = [n(r^2)sin(2pi/n)]/2.

B) Show that limit as n goes to infinity A_n = (pi)(r^2).
For this one, I think that you can use the fact that (sin x)/x = 1

Appreciate it if anyone can contribute anything.
• Mar 22nd 2007, 02:12 PM
ThePerfectHacker
Quote:

Originally Posted by Recklessid
Hello, I was wondering if anyone can help me with this problem.
A) Let A_n be the area of a polygon with n equal sides inscribed in a circle with radius r. By dividing the polygon into n congruent triangles with central angle of (2pi)/n, show that A_n = [n(r^2)sin(2pi/n)]/2.

B) Show that limit as n goes to infinity A_n = (pi)(r^2).
For this one, I think that you can use the fact that (sin x)/x = 1

Appreciate it if anyone can contribute anything.

You want to find,
lim n--> oo (1/2)n(r^2)*sin(2pi/n)