Theorem 5.8c: The area of an {n/k} star inscribed in a circle of radius r is

proof 3: Notice that the triangles in the figure from the proof of Theorem 5.8b

have the same base of 2rsin(180/n), we can get the area of the region we want by multiplying the half of the common base by the difference between the altitudes. That difference is r_k-1, which we know from Theorem 4.3 to be rcos(180k/n)sec(180(k-1)/n).

Return to text

Proof 1

Proof 2

Proof 4

Proof 5

Proof 6