decagon

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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 internal angles equal to 144°. Its Schläfli symbol is {10}.

Construction

A regular decagon is constructible with a compass and straightedge.

• Complete steps 1 through 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. If you cut the angles off the pentagon you will get the shape of a decagon

• 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).

Area

The area of a regular decagon is given by $\backslash \; A\; =\; 2.5dt$ where t is the length of one edge and d is the distance between parallel sides.

d = 2t(cos54° + cos18°) by simple trigonometry.

Petrie polygons

The regular decagon is the Petrie polygon for seven higher dimensional polytopes, shown in these skew orthogonal projections:

150px 5-cube (5D)	150px 6-demicube (6D)

Construction

A regular decagon is constructible using compass and straightedge:

See also

• decagonal number

• Gambrel

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "decagon". The list of authors you can find on this page.