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

**proof**: A horizontal line through the P_{j-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.