Hexagon  (6-gon)

Definition: A polygon with 6 sides
Try this Adjust the hexagon below by dragging any orange dot. You can switch it between a regular and irregular hexagon using the "regular" checkbox.

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
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

Radius equals side length

In a regular hexagon, the radius equals the side length. That is, a line from the center to any vertex will have the same length as any side.

Because of this, a regular hexagon can be thought of as being made of 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.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons