DECAGON

a regular decagon

In geometry, a 'decagon' is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and all angles equal to 144°, therefore making each angle of a regular decagon be 144°. Its Schläfli symbol is {10}.
The area of a regular decagon of side length ''a'' is given by
:A = rac{5}{2}a^2 cot rac{pi}{10} = rac{5a^2}{2} sqrt{5+2sqrt{5}} simeq 7.694208843 a^2.

Contents
Construction
See also
External links

Construction


A regular decagon is constructible with a compass and straightedge.
#Complete steps 1 though 6 of constructing a pentagon.
#Extend a line from each corner of the pentagon through the center of the circle made in step 1 of constructing a pentagon to the opposite side of that same circle.
#The five corners of the pentagon constitute every other corner of the decagon. The remaining five corners of the decagon are those points where the lines of step 2 cross the original circle (but not a pentagon corner).

See also



decagonal number

Gambrel

External links





Definition and properties of a decagon With interactive animation

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