We explain what a polygon is in geometry, the elements that compose it and what types exist. In addition, how its measurements are calculated.
What is a polygon?
In geometry, a polygon is a flat 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 one line crossing another. Its name comes from the Greek words poly (“many”) and gonos (“angle”), that is, they are in principle 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 (plane 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”, since they are figures closed in themselves. You must read about Square Meter once.
There are many types of polygons and many ways of understanding them, depending on whether we are talking about Euclidean or non-Euclidean geometry, but they are usually named according to the number of sides they have, using numerical prefixes. For example, a pentagon (penta + gonos) is a polygon that has five recognizable sides.
The rest of the polygons are named as follows:
Elements of a polygon
Polygons are composed of a series of geometric elements to take into account:
- Sides: These are the straight line segments that make up the polygon, that is, the lines that trace it on the plane.
- Vertices: These are the meeting points, intersections or unions of the sides of the polygon.
- Diagonals: These 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: These are the angles that make up two of its sides or segments in the interior area of the polygon.
- Exterior angles: These are the angles that make up one of its sides or segments and the projection or continuation of another in the exterior area of the polygon.
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. These are polygons 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. In addition, regular polygons are also:
- Equilateral polygons: These are polygons whose sides always measure the same.
- Equiangular polygons: These are polygons whose internal angles always measure the same.
- Irregular polygons: These are polygons 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 cut off at any point:
- Simple polygons: These are those whose lines or sides never intersect or cut off, and therefore have only one contour.
- Complex polygons: These 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: These are simple polygons whose internal angles never exceed 180° of opening. They are characterized because any side can be contained within the figure.
- Concave polygons: These are complex polygons whose internal angles exceed 180° of opening. They are characterized because a straight line is capable of cutting the polygon in more than two different points.
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Measurements of a polygon
Since it is a flat figure, which exists only in the two-dimensional plane (i.e. 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 made:
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 it 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.
Which plane figures are not polygons?
Not all plane figures are polygons. Figures that do not close on themselves (that is, that 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.
