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

**proof**: Consider the following figure.

We can divide the star into n quadrilateral regions formed by
putting the red and green triangles together, as shown above. The red
and green triangle are both isosceles triangles. Since
r_{k-1} = rcos(180k/n)sec(180(k-1)/n) by
Theorem 4.3, the area of the
green triangle is
r^{2}cos^{2}(180k/n)sec^{2}(180(k-1)/n)sin(180/n)cos(180/n)
by Corollary 5.1b. The area of the
red triangle is s^{2}sin(180k/n)cos(180k/n) also by
Corollary 5.1b.