5.9: Convexity
5.9. Convexity
This short section presents a simple result which to some extent justifies the assumptions made in the previous section - namely that the perimeter (or area) of a regular n-gon inscribed in a circle is less than the perimeter (or area) of the circle, and of the circumscribed regular n -gon.
Problem 212 A convex polygon P 1 is drawn in the interior of another convex polygon P 2 .
(a) Explain why the area of P 1 must be less than the area of P 2 .
(b) Prove that the perimeter of P 1 must be less than the perimeter of P 2 .