Do you need to calculate the area of a regular pentagon or its apothem and you don't know the formula? No problem thanks to our online tool.
It is only necessary to know the length of one side of this polygon and enter its value in the online calculator. After pressing the calculate button, you will get the area and the value of its apothem.
Apothema of a pentagon
¿What is the apothem of a pentagon?? In a regular polygon, the distance from any of its sides to the center of the figure is called apothem. Thanks to this, it is easy to obtain how much is the apothem of a regular polygon by applying a couple of formulas that we calculate automatically for you.
How to extract the apothem of a pentagon
To calculate the apothem of a pentagon or any other regular polygon with N sides we can use several mathematical formulas.
First method to calculate the apothem
The first of these is as follows:
- a: the value of the apothem that we have to calculate.
- rdistance from the center of the polygon to one of the vertices of the polygon
- l: measure of one of the sides of the polygon
Second method to extract the apothem
If we are missing any data from the above formula, here is an equally valid alternative:
In this case we have:
- apthe value of the apothem
- Lthe length of one of the sides
- αis the value of the central angle, that is, the value of the angle formed by the two lines resulting from joining the center of the polygon with two consecutive vertices. The value of the central angle can be calculated by dividing 360º by the number of sides of the polygon. In other words:
α = 360º / N
Since the pentagon has five sides, N will be equal to 5, which gives us a 72º central angle.
For example, if we have a pentagon with a side of 5 centimeters, the value of its apothem will be:
ap = 5 cm / [2tan(36º)] = 3.44 centimeters
The area of a pentagon and its apothem are related to each other, so that to calculate the area of the pentagon we must know its value as can be seen in the following formula:
Let's see what is the area of the pentagon of the previous example whose side was equal to 5 cm:
Area = (5 x 5 cm x 3,44 cm) / 2 = 43 cm2
If we do not know the value of the apothem and we don't want to calculate it, we can apply this other formula to calculate the area of a regular pentagon:
Area = 1.72 x L2
If you have any questions about how to extract the apothem or calculate the area of a regular pentagonLeave us a comment and we will solve your problems as soon as possible.