1. [5] A regular 2022-gon has perimeter 6.28. To the nearest positive integer, compute the area of the 2022-gon.
Answer:
\begin{tabular}{|l|}
\hline 3 \\
\hline
\end{tabular}
Solution: Note that the area of a regular 2022-gon is approximately equal to the area of its circumcircle, and the perimeter of a regular 2022-gon approximately equals the perimeter of its circumcircle. Since the perimeter is $6.28 \approx 2 \pi$, the circumradius $R \approx 1$, so the area of the 2022-gon is approximately $R^{2} \pi \approx \pi \approx 3$