The word apothem has its origin in a Greek word that, when translated into Spanish, is understood as "come down" or "depose". In the field of geometry, this term is used to name the shortest path that separates the central point of the regular polygons from any of their respective sides.
It can be said, therefore, that the apothem of regular polygons constitutes a segment that extends from the central axis of the figure to the middle of some of its sides. The apothem, in short, is in all cases perpendicular to the side in question. It can also be taken into account that polygons are closed geometric figures that are made up of straight line segments and consecutive characters (but are not aligned), which are called sides. When all the sides and the respective angles of the figure are identical, we speak of a polygon of regular type.
It should be noted that the apothem is complemented by the sagite (as the line fragment that arises from the central point of the arc of a circle and that of its corresponding chord is known) to compose the radius. The radius, on the other hand, identifies all the segments that go from the central axis to any point on the circumference.
To understand these three concepts graphically, it is first necessary to imagine a circumference; then, place within it (and formed with four of its own points) a square, so that if it were drawn larger it would exceed the surface of the circumference. With these two figures in mind, if you start from the center of the first one to trace its radius and pass through the midpoint of one of the four sides of the square, then three segments will be appreciated: one from the center to the side, which is called apothem ; another, from the side to the limit of the circumference, or the sagite ; and finally, the sum of both results in the segment called radius .
It is interesting to know that the apothem, the sagite and the radius allow various measurements to be carried out to obtain data linked to the polygons. For this, different formulas are used to define the variables.
In pyramids of a regular character, the apothem constitutes the height of their triangular faces. According to experts in the field, it is the segment that joins the vertex with the central part of any of the sides of the polygon that constitute its base. The apothem, therefore, comes to coincide with the height of each of the triangular faces.
First of all, it is necessary to note that n is equal to the number of sides that the polygon in question has. Therefore, it is possible to deduce that the value of α is obtained simply by dividing 360 ° by n. If we take as an example a side that is equal to unity, then we can easily find a list of numbers that help to calculate the apothem of any regular polygon, just starting from the value of one side. The image also shows the angles required for some of the more common polygons.
After solving the equation in this way, a table is obtained that returns the value of the apothem for each type of regular polygon (triangle, square, etc.) whose sides are equal to unity. Thus, to calculate any apothem, it will be enough to multiply the value corresponding to the type of polygon by the measure of the side in question.