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Decagon

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The constructible regular 10-sided polygon with Schläfli symbol {10}. The inradius r, circumradius R, and area can be computed directly from the formulas for a general regular polygon with side length s and n=10 sides,

r=1/2scot(pi/(10))
(1)
=1/2sqrt(5+2sqrt(5))s
(2)
R=1/2scsc(pi/(10))=1/2(1+sqrt(5))s
(3)
=phis
(4)
A=1/4ns^2cot(pi/(10))
(5)
=5/2sqrt(5+2sqrt(5))s^2.
(6)

Here, phi is the golden ratio.

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