Decagon
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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 1440°, therefore making each angle of a regular decagon be 144°. Its Schläfli symbol is . The area of a regular decagon of side length a is given by
- [A = \fraca^2 \cot \frac = \frac \sqrt} \simeq 7.69421 a^2.]
Constructing a decagon
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
External links
- , [Decagon] at MathWorld.
Polygons Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Heptadecagon | Enneadecagon | Icosagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon
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