What is a nonagon?

A nonagon or 9-gon is a nine-sided polygon with nine internal angles that amount to 1260°. A nonagon is likewise called an enneagon. In numerous ways, enneagon is a more accurate term, since it supplies Greek roots because that both that prefix (ennea-, meaning nine) and suffix (-gon, angled).

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Nonagons room rarely supplied in most geometry texts, but it is an intriguing shape, whether you study a continuous nonagon or an irregular nonagon.


Nonagon shape

To be a nonagon or enneagon, the form must have all these properties:

It have to be two dimensional (planar)It have to use only nine heat segmentsIt should close in one area

The nine heat segments are the nonagons" sides, and also they attach to form the nonagons" angles.


Nonagon sides

A nonagon has nine right sides of equal length. If the sides are all the same length, then you have actually a constant nonagon. If the sides differ in length, climate you have actually an irregular nonagon.


If the sides space curved, it is not a nonagon.

Nonagon angles

Every nonagon has actually nine internal angles that sum to 1260°, and also the nine exterior angle of a nonagon amount to 360°.


Every an easy nonagon (not complex) can have it"s interior separated into seven triangles.


You can uncover the sum of inner angles by multiplying 7 × 180°, i m sorry is exactly how you acquire 1260°.

Nonagon diagonals

Because every diagonal has 9 interior angles that connect, a nonagon has actually 27 diagonals.


Regular nonagon

A continuous nonagon shape has actually 9 equal sides and 9 congruent angles. In a constant nonagon, each inner angle measures 140°.

A continual nonagon is a subtle and also beautiful design:


It is very nearly a circle, however not quite. The internal angles room each 140°. You deserve to verify this due to the fact that 1260° ÷ 9 (angles) = 140°.

The main angle is 40° (which you have the right to calculate by separating 360° through 9). This method you deserve to construct a constant nonagon v 7 isosceles triangles v two angles of 70° and also one edge of 40°.

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Irregular nonagon

Irregular nonagons deserve to have sides of various lengths and also interior angles of differing sizes. Yet, also odd shapes prefer these are nonagons:


A polygon v at least one internal angle higher than 180° is a concave polygon and always created an rarely often rare polygon.