This has been bugging me for a while and I thought that you guys might know an answer. Awhile ago I realized that there is a direct relationship between the radius (as in the distance between a corner and the center) squared and the area of any regular polygon with the same number of sides. For example the radius of any square, squared and multiplied by 2 equals the area. But also, for any triangle the radius squared times approx. 1.3 equals the area.(adsbygoogle = window.adsbygoogle || []).push({});

By finding this for several polygons, I found what I expected, the constant for each polygon as the sides increase approaches 3.14. I also found that there is a constant between the diameter of a polygon and the perimeter which also approaches 3.14 as the number of sides increases on the regular polygon.

My question is, according to these relationships is there a way to determine the value of any of these constants for polygons including a circle (3.14) (assuming that it is a polygon with a infinite number of sides) using an equation? Is there any equation you can think of that shows this? Perhaps there is an equation that determines this from the relation of the radius and the apothum (sp)?

Thanks

-scott

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# Circles and polygons

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