Hexagon - math word definition - Math Open Reference

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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.

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

A regular hexagon is made up of six equilateral triangles:

Regular hexagon showing it is made from six equilateral triangles

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.

Properties of regular hexagons

Properties of all hexagons

The Nuts and Bolts of Hexagons

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons