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vquidor · Jul 19, 2011, 04:50 AM

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/-6cdMKOSZHX...1600/given.JPG

ebaines · Jul 19, 2011, 06:09 AM

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

$<br /> A = nr^2 \tan(\frac {180^{\small o}} n)<br />$

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.