Hexagon definition - Math Open Reference

Hexagon (6-gon)

From Greek: hex "six" + gonia "angle"

Definition: A polygon with 6 sides

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

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

Because a hexagon has an even number of sides, in a regular hexagon, opposite sides are parallel.

Properties of regular hexagons

Interior angle	120°	Like any regular polygon, to find the interior angle we use the formula (180n–360)/n . For a hexagon, n=6. See Interior Angles of a Polygon
Exterior Angle	60°	To find the exterior angle of a regular hexagon, 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	2.598s² approx	Where S is the length of a side. To find the exact area of a hexagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon

Properties of all hexagons

Number of diagonals	9	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	4	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	720°	In general 180(n–2) degrees . See Interior Angles of a Polygon

The Nuts and Bolts of Hexagons

Most nuts and bolt heads are made in the shape of a hexagon. Because a hexagon has three pairs of parallel faces, a wrench can be placed over any pair.

In a confined space, the wrench can be turned 60° (the exterior angle of a hexagon) and then the wrench re-positioned on the next pair of sides. Doing this repeatedly will tighten the nut.

In this way, you do not need room to rotate the entire wrench a full circle.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons