Archimedes' Area of a Circle

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1. How does the area of the inscribed square compare to the area of the circle?

2. How does the area of the inscribed hexagon compare to the area of the circle?

3. How does the increase in n, effect the inscribed polygon's area in comparison to the area of the circle?

4. What is the area of a polygon with n=20? What is the area of the circle?

Elizabeth Phillips, 2 December 2013, Created with GeoGebra