Nonagon — Definition, Regular & Irregular Examples
What is a nonagon?
A nonagon or 9-gon is a nine-sided polygon with nine interior angles that sum to 1260°. A nonagon is also called an enneagon. In many ways, enneagon is a more accurate term, since it uses Greek roots for both its prefix (ennea-, meaning nine) and suffix (-gon, angled).
Nonagons are rarely used in most geometry texts, but it is an intriguing shape, whether you examine a regular nonagon or an irregular nonagon.
Nonagon shape
To be a nonagon or enneagon, the shape must have all these properties:
It must be two dimensional (planar)
It must use only nine line segments
It must close in an area
The nine line segments are the nonagons' sides, and they connect to form the nonagons' angles.
Nonagon sides
A nonagon has nine straight sides of equal length. If the sides are all the same length, then you have a regular nonagon. If the sides vary in length, then you have an irregular nonagon.
If the sides are curved, it is not a nonagon.
Nonagon angles
Every nonagon has nine interior angles that sum to 1260°, and the nine exterior angles of a nonagon sum to 360°.
Every simple nonagon (not complex) can have it's interior divided into seven triangles.
You can find the sum of interior angles by multiplying 7 × 180°, which is how you get 1260°.
Nonagon diagonals
Because every diagonal has 9 interior angles that connect, a nonagon has 27 diagonals.
Regular nonagon
A regular nonagon shape has 9 equal sides and 9 congruent angles. In a regular nonagon, each interior angle measures 140°.
A regular nonagon is a subtle and beautiful design:
It is very nearly a circle, but not quite. The interior angles are each 140°. You can verify this because 1260° ÷ 9 (angles) = 140°.
The central angle is 40° (which you can calculate by dividing 360° by 9). This means you can construct a regular nonagon with 7 isosceles triangles with two angles of 70° and one angle of 40°.
Irregular nonagon
Irregular nonagons can have sides of different lengths and interior angles of varying sizes. Yet, even odd shapes like these are nonagons:
A polygon with at least one interior angle greater than 180° is a concave polygon and always created an irregular polygon.
A self-intersecting nonagon is a complex nonagon.
Irregular nonagons and regular nonagons both share these same facts:
Its nine interior angles sum to 1260°
It has nine sides, even if those sides cross one another.
Its nine exterior angles sum to 3660°
Nonagon shape in real life
Nonagon examples are rare in both the natural and human-made worlds. Two exceptions:
The U.S. Steel Tower in Pittsburgh, Pennsylvania, is an irregular nonagon.
All houses of worship in the Bahá’í faith are regular nonagons.
