Circle/Inscribed n-polygon/Approximation/Exercise

We consider a circle (with radius ${}1$) and regular ${}n$-gons inscribed in the circle.

1. 

   Suppose that a square is inscribed in the circle. Determine its area and its perimeter.

2. 

   Suppose that a regular ${}6$-gon is inscribed. Determine its area and its perimeter.

3. The area of an inscribed regular ${}n$-gon is an approximation for the area of the circle and its perimeter is an approximation for the circumference of the circle. Which one is better?

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