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Regular Decagon

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RegularDecagon

The regular decagon is constructible 10-sided regular 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.

See also

Decagon, Decagram, Dodecagon, Golden Triangle, Hendecagon, Polygon, Regular Polygon, Trigonometry Angles--pi/10

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References

Dixon, R. Mathographics. New York: Dover, p. 18, 1991.

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Regular Decagon

Cite this as:

Weisstein, Eric W. "Regular Decagon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RegularDecagon.html

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