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Decagon
 
 
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In geometry
Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
, a decagon is any polygon
Polygon

In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
 with ten sides and ten angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
s, and usually refers to a regular
Regular polygon

A regular polygon is a polygon which is Equiangular polygon and equilateral . Regular polygons may be convex or Star polygon....
 decagon, having all sides of equal length and all internal angles equal to 4π/5 (144°). Its Schläfli symbol
Schläfli symbol

In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
 is . The area
Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
 of a regular decagon of side length a is given by

gular decagon is constructible
Constructible polygon

In mathematics, a constructible polygon is a regular polygon that can be Compass and straightedge constructions. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not....
 with a compass and straightedge
Compass and straightedge

Compass-and-straightedge or ruler-and-compass construction is the construction of lengths or angles using only an Idealization ruler and Compass ....
.
  1. Complete steps 1 through 6 of constructing a pentagon
    Pentagon

    In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
    .
  2. Extend a line from each corner of the pentagon through the center of the circle
    Circle

    A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
     made in step 1 of constructing a pentagon
    Pentagon

    In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
     to the opposite side of that same circle.
  3. The five corners of the pentagon constitute every other corner of the decagon.






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    In geometry
    Geometry

    Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers....
    , a decagon is any polygon
    Polygon

    In geometry a polygon is traditionally a plane Shape that is bounded by a closed curve path or circuit, composed of a finite sequence of straight line segments ....
     with ten sides and ten angle
    Angle

    In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
    s, and usually refers to a regular
    Regular polygon

    A regular polygon is a polygon which is Equiangular polygon and equilateral . Regular polygons may be convex or Star polygon....
     decagon, having all sides of equal length and all internal angles equal to 4π/5 (144°). Its Schläfli symbol
    Schläfli symbol

    In mathematics, the Schl?fli symbol is a notation of the form that defines regular polytopes and tessellations.The Schl?fli symbol is named after the 19th-century mathematician Ludwig Schl?fli who made important contributions in geometry and other areas....
     is . The area
    Area

    Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron....
     of a regular decagon of side length a is given by

    Construction

    A regular decagon is constructible
    Constructible polygon

    In mathematics, a constructible polygon is a regular polygon that can be Compass and straightedge constructions. For example, a regular pentagon is constructible with compass and straightedge while a regular heptagon is not....
     with a compass and straightedge
    Compass and straightedge

    Compass-and-straightedge or ruler-and-compass construction is the construction of lengths or angles using only an Idealization ruler and Compass ....
    .
    1. Complete steps 1 through 6 of constructing a pentagon
      Pentagon

      In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
      .
    2. Extend a line from each corner of the pentagon through the center of the circle
      Circle

      A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
       made in step 1 of constructing a pentagon
      Pentagon

      In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540?....
       to the opposite side of that same circle.
    3. 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

    • decagonal number
      Decagonal number

      A decagonal number is a figurate number that represents a decagon. The decagonal number for is given by the formulawith . The first few decagonal numbers are...
    • Gambrel
      Gambrel

      File:Gambrel.jpgA gambrel roof is a type of roof similar to a hip roof but with gables forming the top part of the end slopes....


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