We explain what a polygon is in geometry, the elements that make it up and what types exist. Also, how its measurements are calculated.

## What is a polygon?

In geometry, a polygon is called **a plane geometric figure, composed of a set of line segments connected in such a way that they enclose and delimit a region of the plane** generally without crossing one line with another. Its name comes from the Greek words *poly* (“a lot”) and *gonos* (“angle”), that is, in principle they are geometric figures with numerous angles, although today it is preferred to classify them according to their number of sides and not angles.

Polygons are two-dimensional figures (flat equivalents of three-dimensional polytopes), that is, they have only two dimensions: length and width, and both are determined by the proportions of the lines that compose them. The fundamental thing about a polygon is that the set of its lines separates a region of the plane from the rest, that is, it delimits an “inside” and an “outside”, given that they are figures closed in themselves.

There are many types of polygons and many ways to understand them, depending on whether we are talking about Euclidean or non-Euclidean geometry, but ** are usually named depending on the number of sides they have, using numerary prefixes**. For example, a pentagon (*penta* + *gonos*) is a polygon that has five recognizable sides.

The rest of the polygons are named as follows:

Number of sides | Polygon name |

3 | Trine or triangle |

4 | Tetragon or quadrilateral |

5 | Pentagon |

6 | Hexagon |

7 | Heptagon |

8 | Octagon or octagon |

9 | Nonagon or enneagon |

10 | Decagon |

11 | Endecagon or undecagon |

12 | Dodecagon |

13 | Tridecagon |

14 | Tetradecagon |

15 | Pentadecagon |

16 | Hexadecagon |

17 | Heptadecagon |

18 | Octodecagon or octadecagon |

19 | Nonadecagon or eneadecagon |

20 | Isodecagon or icosagon |

21 | Henicosagon |

22 | Doicosagon |

23 | Triaicosagon |

24 | Tetraicosagon |

25 | Pentaicosagon |

30 | Triacontagon |

40 | Tetracontagon |

50 | Pentacontagon |

60 | Hexacontagon |

70 | Heptacontagon |

80 | Octocontagon or octacontagon |

90 | Nonacontagon or eneacontagon |

100 | hexagon |

1,000 | Chiliágono or kiliágono |

10,000 | Myriagon |

See also: Polyhedra

## Elements of a polygon

Polygons are made up of a series of geometric elements to take into account:

**Sides**. They are the line segments that make up the polygon, that is, the lines that trace it in the plane.**Vertices**. They are the meeting points, intersection or union of the sides of the polygon.**Diagonals**. They are straight lines that join two non-consecutive vertices within the polygon.**Center**. Present only in regular polygons, it is a point in its interior area that is equidistant from all its vertices and sides.**interior angles**. They are the angles that two of its sides or segments make up in the interior area of the polygon.**Exterior angles**. They are the angles that make up one of its sides or segments in the outer area of the polygon and the projection or continuation of another.

## Types of polygons

Polygons are classified in different ways, depending on their specific shape. First of all, it is important to distinguish between regular and irregular polygons:

**regular polygons**. They are those whose sides and internal angles have the same measurement, being equal to each other. They are symmetrical figures, such as the equilateral triangle or the square. Furthermore, regular polygons are at the same time:

**Equilateral polygons**. They are those polygons whose sides always measure the same.**equiangular polygons**. They are those polygons whose internal angles always measure the same.

**irregular polygons**. They are those whose sides and internal angles are not equal to each other, since they have different measurements. For example, a scalene triangle.

On the other hand, polygons can be simple or complex, depending on whether their sides intersect or dry at some point:

**Simple polygons**. They are those whose lines or sides never intersect or intersect, and therefore have a single contour.**Complex polygons**. They are those that present a crossing or intersection between two or more of their non-consecutive edges or sides.

Finally, we can distinguish between convex and concave polygons, depending on the general orientation of their shape:

**Convex polygons**. They are those simple polygons whose internal angles never exceed 180° opening. They are characterized because any side can be contained within the figure.**Concave polygons**. They are those complex polygons whose internal angles exceed 180° opening. They are characterized because a line is capable of cutting the polygon at more than two different points.

## Measurements of a polygon

Being a flat figure, which exists only in the two-dimensional plane (that is, length and width), but closed in itself, polygons contain a segment of the plane and delimit an outside and an inside. Thanks to this, two types of measurements can be carried out:

**The perimeter**. It is the sum of the length of all the sides of the polygon, and in the case of regular polygons it is calculated by multiplying the length of its sides by the number of these.

**The area**. It is the portion of the plane delimited by the sides of the polygon, that is, its “interior” area. Its calculation, however, requires different procedures, for example:

- In a triangle, it is calculated by multiplying the base and the height and dividing by 2.
- In a regular quadrilateral (square), it is calculated by squaring the length of any of its sides.
- In a right quadrilateral (rectangle), it is calculated by multiplying its base by its height.

## What plane figures are not polygons?

Not all plane figures are polygons. **Those figures that do not close on themselves** (that is, they do not have an interior area), **that have curved lines in their formation or whose non-consecutive sides intersect** should not be considered as polygons.

Continue with: Cartesian plane

#### References

- “Polygon” in Wikipedia.
- “Etymology of Polygon” in the Online Spanish Etymological Dictionary.
- “What are polygons?” in the Junta de Andalucía (Spain).
- “The polygons” (video) in Smile and Learn.
- “Polygon (mathematics)” in The Encyclopaedia Britannica.