In
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
, a decagon (from the Greek δέκα ''déka'' and γωνία ''gonía,'' "ten angles") is a ten-sided
polygon
In geometry, a polygon () is a plane figure that is described by a finite number of straight line segments connected to form a closed '' polygonal chain'' (or ''polygonal circuit''). The bounded plane region, the bounding circuit, or the two t ...
or 10-gon.
[.] The total sum of the
interior angles
In geometry, an angle of a polygon is formed by two sides of the polygon that share an endpoint. For a simple (non-self-intersecting) polygon, regardless of whether it is convex or non-convex, this angle is called an interior angle (or ) if ...
of a
simple decagon is 1440°.
A
self-intersecting ''regular decagon'' is known as a
decagram Decagram may refer to:
* 10 gram, or 0.01 kilogram
The kilogram (also kilogramme) is the unit of mass in the International System of Units (SI), having the unit symbol kg. It is a widely used measure in science, engineering and commerce world ...
.
Regular decagon
A ''
regular
The term regular can mean normal or in accordance with rules. It may refer to:
People
* Moses Regular (born 1971), America football player
Arts, entertainment, and media Music
* "Regular" (Badfinger song)
* Regular tunings of stringed instrum ...
decagon'' has all sides of equal length and each internal angle will always be equal to 144°.
Its
Schläfli symbol
In geometry, the Schläfli symbol is a notation of the form \ that defines regular polytopes and tessellations.
The Schläfli symbol is named after the 19th-century Swiss mathematician Ludwig Schläfli, who generalized Euclidean geometry to mor ...
is and can also be constructed as a
truncated pentagon
In geometry, a pentagon (from the Greek language, Greek πέντε ''pente'' meaning ''five'' and γωνία ''gonia'' meaning ''angle'') is any five-sided polygon or 5-gon. The sum of the internal angles in a simple polygon, simple pentagon is ...
, t, a quasiregular decagon alternating two types of edges.
Side length
The picture shows a regular decagon with side length
and radius
of the
circumscribed circle
In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.
Not every poly ...
.
* The triangle
has to equally long legs with length
and a base with length
* The circle around
with radius
intersects