Decagon
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An image of 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°. Its Schläfli symbol is {10}. The area of a regular decagon of side length a is given by
- <math>A = \frac{5}{2}a^2 \cot \frac{\pi}{10} = \frac{5a^2}{2} \sqrt{5+2\sqrt{5}} \simeq 7.69421 a^2.<math>
Constructing a decagon
A regular decagon is constructible with a straightedge and compass.
- Complete steps 1 though 6 of Contructing a pentagon.
- Extend a line from each corner of the pentagon through the center of the circle made in step 1 of Contructing 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).