Theorem 5.4a: The area of the region in the figure above is

sj2 sin(180j/n)cos(180j/n) + sj-12sin(180(j-2)/n)cos(180(j-2)/n)

proof: A horizontal line through the Pj-1 points will divide the region into two isosceles triangles, and we can then apply Corollary 5.1b. We know that half of the vertex angle in the top triangle is 90 - 180j/n, and that half of the vertex angle in the bottom triangle is 90 - 180(j- 2)/n by Theorem 4.1.

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