Calculate area and apothem of pentagon

Calculate apothem and area of a pentagon

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

Pentagon area and apothem calculator

¿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:

Formula to extract the apothem

Being:

  • 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:

Formula for calculating apothem

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

Pentagon area

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:

Pentagon area

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.

14 thoughts on “Calcular área y apotema del pentágono”

  1. Please I need to solve the following exercise. Rosita wants to make a pentagonal floor room with apothem of two. can you calculate the measure of each side?

    Reply
    • Hello Jacqueline,

      If we are asked to calculate the sides of the pentagon from the apothem, we will use this formula:

      Side = apothem x 2tan(36º).

      Therefore, if we are told that the apothem is equal to 2, we have that:

      Side = 2 x 2tan(36º) = 2.906170112

      We hope you find it useful

    • Hello,

      To calculate the area and length of an irregular pentagon we have to use an alternative method that consists of:

      To calculate the length, if you know the area of each triangle, you can also get the length of the irregular pentagon.

      There is another method to do this using the Gaussian determinant but it is more complex.

      If you have any doubts, let us know and we will help you.

      Greetings!

    • Hello Martinez:

      To find the perimeter of a pentagon you only have to multiply by 5 the measure of its side. That is to say:

      5 x 12 cm = 60 centimeters

      As for the area, you just have to apply the formula that we have put in the explanation. You get that the figure has an area of 247.80 cm.2

  2. Hello, if I need to get the apothem of a Pentagon and I only have the measure of one of its sides which is 10 and the measure of the radius is 8.5, how do I do it?

    Reply
    • Hello Eduardo,

      Did the calculator not work for you to obtain the result? The exercise you mention is quite simple to solve and you only have to apply the following formula:

      apothem = 10 cm / [2tan(36º)] = 6.88 centimeters

      Greetings!

  3. Thank you very much for this content I need it for mathematics and it was very helpful, seriously thank you very much for the person who created this content, it was very useful.

    Reply
  4. I want to get the apothem of a pentagon if it says that its area is 15 cm and its perimeter is 10cm and what would be the measure of its side.

    Reply
  5. the following data correspond to a regular pentagon whose side measures 12cm
    side=12cm
    apothem=10.4cm
    perimeter=60cm
    area=374.12cm(in the result of the area I think it is wrong so it comes in the book)
    if the side length varies as indicated below complete the following table
    side=24-36-48-60-14.4-6-4-3, all are cm.
    these are the quantities in the table but I have to get apothem in cm, perimeter in cm, and area in cm. can you help please it is urgent thanks

    Reply

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