Decagon definition - Math Open Reference

Decagon (10-gon)

From Greek deka "ten" + gonia "angle"

Definition: A polygon with 10 sides

Try this Adjust the decagon below by dragging any orange dot. By clicking on the top left command line, you can switch it between a regular and irregular decagon.

(If there is no image below, see support page.)

Properties of regular decagons

Interior angle	144°	Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a decagon, n=10. See Interior Angles of a Polygon
Exterior Angle	36°	To find the exterior angle of a regular decagon, we use the fact that the exterior angle forms a linear pair with the interior angle, so in general it is given by the formula 180-interior angle. See Exterior Angles of a Polygon
Area	7.694s² approx	Where S is the length of a side. To find the exact area of a decagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon

Properties of all decagons

Number of diagonals	35	The number of distinct diagonals possible from all vertices. (In general ½n(n–3) ). In the figure above, click on "show diagonals" to see them. See Diagonals of a Polygon
Number of triangles	8	The number of triangles created by drawing the diagonals from a given vertex. (In general n–2). In the figure above, click on "show triangles" to see them. See Triangles of a Polygon
Sum of interior angles	1440°	In general 180(n–2) degrees . See Interior Angles of a Polygon

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons