The notion of apothem is used in geometry.
Apothem is a word derived from a Greek word that, when translated into Spanish, is understood as "to lower" or "to depose" . In the field of geometry , this term is used to name the shortest path that separates the central point of regular polygons from any of their respective sides .
It can therefore be said that the apothem of regular polygons constitutes a segment that extends from the central axis of the figure to the middle of one 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 consecutive straight line segments (but not aligned), which are called sides. When all the sides and the respective angles of the figure are identical, we speak of a regular polygon.
It is worth noting that the apothem is complemented by the sagitta (as the fragment of a straight line that arises from the central point of the arc of a circumference 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.
Concept of apothem
To graphically understand these three concepts, it is necessary first of all to imagine a circle; then, to 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 circle. With these two figures in mind, if we start from the center of the first to draw its radius and go through the midpoint of one of the four sides of the square, then we will see three segments: one from the center to the side, which is called the apothem; another, from the side to the limit of the circle, or the sagitta; and finally, the sum of both results in the segment called the radius.
It is interesting to know that the apothem, the sagitta and the radius allow various measurements to be carried out to obtain data related to polygons. For this, different formulas are used that allow the variables to be defined.
In regular pyramids , the apothem is the height of the 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, coincides with the height of each of the triangular faces.
The apothem is the shortest path that links the central point of regular polygons with any of its sides.
Troubleshooting
When dealing with a problem involving regular polygons , it is very common to overlook the way in which the apothem relates to the side, which can result in an error of varying importance. However, by simply using the apothem table , it is possible to perform the calculation simply by taking into account the chosen side. The formula shown in the image shows the trigonometric relationship in question.
First of all, it is necessary to notice 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 one, then we can easily find a list of numbers that help us 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 most common polygons.
After solving the equation in this way, we obtain a table that returns the value of the apothem for each type of regular polygon (triangle, square, etc.) whose sides are equal to one. Thus, to calculate any apothem, it will be enough to multiply the value corresponding to the type of polygon by the measurement of the side in question.