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.

Related polygon topics

General

Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons

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