Areas of Circles Observation

Below are several circles, all with radius=2, with inscribed polygons. Look at the areas of each of the polygons.

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Questions to consider:
Toward what number do the areas seem to be merging to?
Calculate the area of a circle with radius=2. What does this tell us about the areas of circles with respect to inscribed polygons?

Brian Bisignani, July 10, 2008, Created with GeoGebra