Heptagon  (7-gon)

Definition: A polygon with 7 sides
also: Septagon
Try this Adjust the heptagon below by dragging any orange dot. By clicking on the top left command line, you can switch it between a regular and irregular heptagon.

Properties of regular heptagons

Interior angle 128.571° Like any regular polygon, to find the interior angle we use the formula   (180n–360)/n . For a heptagon, n=7. See Interior Angles of a Polygon
Exterior Angle 51.429° To find the exterior angle of a regular heptagon, 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 3.633s2
Where S is the length of a side. To find the exact area of a heptagon or any polygon, using various methods, see Area of a Regular Polygon and Area of an Irregular Polygon

Properties of all heptagons

Number of diagonals 14 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 5 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 900° In general 180(n–2) degrees . See Interior Angles of a Polygon

Heptagonal coins

Heptagons are not seen much in everyday life except in the UK, where there are coins in the shape of a heptagon. On the right is the 50 pence coin. It is not a strict heptagon because the sides are actually curved arcs instead of straight lines. The resulting shape is known as an "Equilateral Curve Heptagon".

It has one very curious property; in spite of not being a circle it has the same diameter everywhere! This is done so that it will always fit in coin-operated machines, but still feel different in the hand from other round coins - a help to sight-impaired people.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons