A regular polygon is a figure whose interior angles and sides are equal.
Polygon is a concept that comes from the Greek language, whose meaning can be understood as "many angles" . It is a flat figure of geometry that is formed from the union of straight segments known as sides .
According to their characteristics, it is possible to speak of different types of polygons. Regular polygons are those whose sides and interior angles are equal . This means that all the sides measure the same, as do the angles formed by the unions of these segments.
These properties , on the other hand, make all regular polygons equilateral polygons (with sides of identical length) and equiangular (all of their interior angles measure the same). Furthermore, the regular polygon can be inscribed in a circle; This means that it is possible to draw a circle (called circumscribed ) that passes through all its points, so that it contains it completely within it.
Regular polygon example
An example of a regular polygon, therefore, is a square whose sides measure 5 centimeters each and its interior angles measure 90º each. Other regular polygons are equilateral triangles , regular hexagons , and regular pentagons .
To calculate how much the interior angles of a regular polygon measure, you can use the following formula : (n-2) x 180 degrees / n . If we take the case of a square, we would solve the unknown as follows (since the number of sides or n is equal to 4 ):
(4-2) x 180 degrees / 4
2 x 180 degrees / 4
360 degrees / 4
90 degrees
This formula allows us to confirm that the interior angles of a square measure ninety degrees each .
It should be noted that there are multiple formulas to calculate other characteristics of regular polygons, such as their area or exterior angles.
A regular polygon is equiangular and equilateral .
Main elements
An extensive list of elements make up the regular polygon, as follows:
* vertex : each point that must be joined to appreciate the shape of the polygon;
* side : each segment that forms it and that results from the union of two vertices;
* center : the point that is the same distance from all vertices;
* radius : any segment resulting from joining a vertex and the center;
* apothem : a segment that starts from the center and ends on either side, so that it is perpendicular to the latter;
* diagonal : any segment joining a pair of non-contiguous vertices;
* perimeter : as in other figures, the sum of the extension of each of its sides;
* semiperimeter : half the value of the perimeter;
* sagitta : a segment that is formed starting from the point of the apothem that is on one side and ending at the arc of circumference. The sum of this element and the apothem results in a segment of equal length to the radius.
Diagonals of a regular polygon
There is a formula that allows us to find the number of diagonals of any regular polygon, which is based on the following two fundamentals:
* From each of the vertices of a regular polygon there are (n – 3) diagonals, with n being the number of vertices. The 3 represents the vertices with which it can never be joined through a diagonal, which are the two adjacent ones and itself;
* It is necessary to divide by two the sum obtained by applying the previous reasoning , since it would give us twice each diagonal (example: one that goes from point A to B, and the one that is formed from B to A).
Having understood this explanation, we come up with the formula Nd = n(n – 3) / 2 , which can be read as the number of diagonals Nd is equal to dividing by 2 the product of the number of vertices n times (n – 3).