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Information About

Decagonal




In Geometry , a decagon is any Polygon with ten sides and ten Angle s, 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+2\sqrt{5}} \simeq 7.694208843 a^2.

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).


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