**Theorem 5.3b**: The perimeter of the quadrilateral region in
the figure above is

2rcos(180k/n)sin(360/n)sec(180j/n)sec(180(j-2)/n).
**proof**: From Theorem
4.4a we know that

s_{j} = rcos(180k/n)[tan(180j/n) -
tan(180(j-1)/n)]
and

s_{j-1} = rcos(180k/n)[tan(180(j-1)/n) -
tan(180(j-2)/n)]
Hence

s_{j} + s_{j-1} = rcos(180k/n)[tan(180j/n)
- tan(180(j-2)/n)]
which is the distance from a P_{j} point to a
P_{j-2} point, as one could see from looking at the figure.
Thus, by Theorem 4.4b,

2(s_{j} + s_{j-1}) =
2rcos(180k/n)sin(360/n)sec(180j/n)sec(180(j-2)/n)
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