Circle/Inscribed npolygon/Approximation/Exercise
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We consider a circle (with radius ) and regular gons inscribed in the circle.

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

Suppose that a regular gon is inscribed. Determine its area and its perimeter.
 The area of an inscribed regular 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?