Decagon

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Decagon

In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°.

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• Decagon - Wikipedia

  In geometry, a decagon (from the Greek δέκα déka and γωνία gonía, "ten angles") is a ten-sided polygon or 10-gon. The total sum of the interior angles of a simple decagon is 1440°. ## Regular decagon [edit] A regular decagon has all sides of equal length and each internal angle will always be equal to 144°. Its Schläfli symbol is {10} and can also be constructed as a truncated "Truncation (geometry)") pentagon, t{5}, a quasiregular decagon alternating two types of edges. Decagons often appear in tilings with (partial) 5-fold symmetry. The images show an Islamic geometric pattern (15th century), an illustration in Kepler's Harmonices Mundi (1619) and a Penrose tiling. ### Side length [edit] [...] Regular decagon dissected into 10 rhombi | 5-cube | | ## Skew decagon [edit] 3 regular skew zig-zag decagons | {5}#{ } | {5/2}#{ } | {5/3}#{ } | | | A regular skew decagon is seen as zig-zagging edges of a pentagonal antiprism, a pentagrammic antiprism, and a pentagrammic crossed-antiprism. | A skew decagon is a skew polygon with 10 vertices and edges but not existing on the same plane. The interior of such a decagon is not generally defined. A skew zig-zag decagon has vertices alternating between two parallel planes. [...] : {\displaystyle A=10\tan \left({\frac {\pi }{10}}\right)r^{2}=2r^{2}{\sqrt {5\left(5-2{\sqrt {5}}\right)}}\simeq 3.249196962\,r^{2}} In terms of the circumradius R, the area is: : {\displaystyle A=5\sin \left({\frac {\pi }{5}}\right)R^{2}={\frac {5}{2}}R^{2}{\sqrt {\frac {5-{\sqrt {5}}}{2}}}\simeq 2.938926261\,R^{2}} An alternative formula is {\displaystyle A=2.5da} where d is the distance between parallel sides, or the height when the decagon stands on one side as base, or the diameter of the decagon's inscribed circle. By simple trigonometry, : {\displaystyle d=2a\left(\cos {\tfrac {3\pi }{10}}+\cos {\tfrac {\pi }{10}}\right),} and it can be written algebraically as : {\displaystyle d=a{\sqrt {5+2{\sqrt {5}}}}.} ### Construction [edit]

• Decagon: meaning, properties, and uses of a sacred shape

  The decagon, a polygon with ten equal sides, is an emblematic figure of sacred geometry. It symbolizes inner harmony, completeness, and the power to anchor intentions in matter. The number 10, which composes it, carries a vibration of accomplishment, realization, and perfect balance between the spiritual and earthly worlds. Since ancient times, this fascinating shape has been used in various spiritual and esoteric traditions for its powerful waveforms. In dowsing, radionics, but also in meditation and energy purification practices, the decagon acts as a true amplifier of subtle energy. [...] The decagon is one of the most powerful geometrical tracings, tuned to the 10 fingers of the hand and neutralizing all discordances. It can thus contribute to the realization of a beneficial program. It can be used to purify your crystal and your witnesses before any new programming; it has the particularity of canceling all negative elements. The triple decagon emits increased power. [...] In geometry, a decagram is a star polygon with 10 vertices. There is only one regular decagram, which can be constructed from the regular decagon by connecting the vertices 3 by 3. A decagon is a polygon with ten sides and ten interior angles. It is derived from the Latin words "deka", meaning ten, and "gonia", meaning angle. A defining characteristic of a decagon is that all its sides have equal lengths and all its interior angles have equal measures. The sum of a decagon's interior angles is 1440 degrees, with each angle measuring 144 degrees.

• Decagon | Definition, Sides & Shape - Lesson | Study.com

  ## Lesson Summary Decagons are polygons that contain ten sides and ten vertices. As polygons, decagons must be closed and composed only of straight lines. Lines intersect at the vertices, creating the decagon's ten interior angles. In most decagons, these will add to a total of 1440 degrees. In a regular decagon, all sides and interior angles are equal. In an irregular decagon, not all sides and angles are equal. A concave decagon has at least one interior angle measuring greater than 180 degrees, while a convex decagon has no angles greater than 180 degrees. All the lines in a simple decagon only intersect at the vertices, while in a complex decagon the lines intersect themselves elsewhere, creating multiple enclosed spaces. [...] ##### ELM: CSU Math Study Guide ##### Study.com SAT Study Guide and Test Prep ##### SAT Subject Test Mathematics Level 1: Practice and Study Guide ##### Trigonometry: High School ##### Supplemental Math: Study Aid ##### Glencoe Geometry: Online Textbook Help ##### McDougal Littell Geometry: Online Textbook Help ##### Prentice Hall Geometry: Online Textbook Help ##### Amsco Geometry: Online Textbook Help ##### Geometry: High School ##### SAT Subject Test Mathematics Level 2: Practice and Study Guide ##### Holt Geometry: Online Textbook Help ## What Is a Decagon? A decagon is a polygon with ten sides. Polygons are closed two-dimensional shapes with straight lines. This means polygons include triangles, squares, and decagons, but not circles or ovals. [...] ## Regular and Irregular Decagons A decagon is a 10-sided polygon. It also has ten vertices - which is where the sides meet - and ten angles. The regular decagon is probably the most recognizable one. It's called a regular decagon because all its sides and angles are congruent, or equal in size. In this next illustration, the vertices are circled. Regular decagon with the vertices circled. | In a regular decagon, all the angles measure 144 degrees. So, the sum of a regular decagon's angles is always 1,440 degrees. Not all decagons are regular, however. As previously stated, a decagon is simply a 10-sided polygon, so decagons can take on various forms as long as they're closed and have ten sides. This is an irregular decagon because the sides and angles are not congruent:

• DECAGON Definition & Meaning | Dictionary.com

  ## Explanation Vocabulary.com A decagon is a closed shape with ten sides and ten angles. Your geometry teacher would also tell you that a decagon is a polygon. The word decagon comes from Greek roots, deka, or "ten," and gōnia, "angle or corner." Any ten-sided shape can be called a decagon, whether it's a street sign or the doodle you draw in your notebook during math class. Speaking of math class, in geometry you may learn that a "regular decagon" is one with sides that are all equal to each other and with internal angles that all measure 144 degrees. Keep Reading on Vocabulary.com ## Example Sentences Examples are provided to illustrate real-world usage of words in context. Any opinions expressed do not reflect the views of Dictionary.com. [...] Dictionary.com Thesaurus.com Synonyms # decagon American [dek-uh-gon, -guhn] / ˈdɛk əˌgɒn, -gən / ## noun decagons plural 1. a polygon having ten angles and ten sides. decagon British / dɪˈkæɡənəl, ˈdɛkəˌɡɒn / ## noun 1. a polygon having ten sides "Collins English Dictionary — Complete & Unabridged" 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012 decagon Scientific / dĕk′ə-gŏn′ / 1. A polygon having ten sides. ## Other Word Forms ### Derived Forms decagonal adjective decagonally adverb ### Inflected Forms #### Nouns decagons plural ## Etymology ### Origin of decagon From the Medieval Latin word decagōnum, dating back to 1565–75. See deca-, -gon

• Geometric properties of decagon | calcresource

  ### Definitions Decagon is a polygon with ten sides and ten vertices. A decagon, like any other polygon, can be either convex or concave, as illustrated in the next figure. A convex decagon has none of its interior angles greater than 180°. To the contrary, a concave decagon (or polygon) has one or more of its interior angles greater than 180°. A decagon is called regular when its sides are equal and also its interior angles are equal. Having only the sides equal is not adequate, in that matter, since the decagon may be concave, with equal sides. As demonstrated in the figure below, many possible concave decagons can be defined, with equal sides, but unequal interior angles. These decagons are called equilateral. Any decagon that is not regular is called irregular.

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  Q783794