POSSIBLE SOLUTION(S)

1. Inscribed Area = n/2 Sin[2 Pi / n].

2. Circumscribedarea = n Tan[Pi/n]

3. At n = 400, there are three decimal places of accuracy in both the Inscribed and Circumscribed cases. The average of the two values yields four decimal places of accuracy.

4. The easiest method of solution is by trial and error (see note in ISSUES IN SOLUTIONS.)

5. While one could use ListPlot, we simply graph the curves that go through the data points.

6. By sight from the curves graphed to the solution to problem #5, it appears that the circumscribed area converges to Pi faster than the inscribed area. Below we also plot the differences to see which ones go to zero first.