Calculate area and apothem of a regular hexagon

Calculates without formulas the area of a regular hexagon and its apothem. Regular means that all sides are equal, an important factor for our online tool to work properly and provide the result you are looking for.

If you want to to know the area of a regular hexagonSimply enter the value of one of its sides, press the calculate button and you're done. It's that easy. Remember that we have multiple math calculators to facilitate those simple calculations that require the use of formulas that we have already forgotten in some corner of our brain.

How to calculate the apothem of a regular hexagon

Hexagon area and apothem calculator

For calculate the apothem of a regular hexagon there are several methods.

Formula of the apothem of the hexagon

The first is to apply this formula:

Formula to extract the apothem

Being:

  • a: the value of the apothem of the hexagon
  • l: the measure of one of the sides of the regular polygon
  • r: in the case of the hexagon, we will also write here the length of the hexagon side.

The equality of l=r will make the above formula simpler so that we can calculate the apothem of a regular hexagon by solving the following equation:

Formula for calculating the apothem of a regular hexagon

With the Pythagorean Theorem

Apothem of a hexagon

Another method for to draw the apothem of the hexagon consists of using the Pythagorean Theorem. If you look at the image above, the apothem shape (a) forms a right triangle with R (the side) and L/2 (half a side). If we translate this to Pythagoras, we have this formula:

a2 + (l/2)2 = l2

From there we clear the unknown a and it will give us how long the apothem of the hexagon is. For example, let's solve an exercise in which we are asked to calculate the apothem of a regular hexagon whose side measures 5cm. We apply the above formula and we have that:

a2 + (2,5)2 = 52
a2 + 6,25 = 25
a2 = 25 – 6,25 = 18,75
a = √18.75 = 4.33 centimeters

With the central angle

We are going to tell you a third method to obtain the apothem of a hexagon from the length of its side and the value of the central angleWhat is this angle? It is the angle formed by two lines that start from the center of the figure towards two consecutive vertices.

The value of the central angle is calculated with this formula:

α = 360º / N

where N we write the number of sides that the figure has and that in our case is equal to six. Therefore:

α = 360º / 6 = 60º

Now all we have to do is substitute the data we know in the following formula which will give us the length of ap:

Formula for calculating apothem

Remember:

  • L is the length of the side
  • α is the value of the central angle, which in our case is 60 degrees.

Simply substitute and solve the equation.

How to calculate the area of a hexagon

For calculate the area of a hexagon we have to apply this formula:

Area of the hexagon = 3 - Side - apothem

That is, you simply have to calculate the triple of the multiplication of one of the sides by the apothem of the regular hexagon.

Calculate the area of the hexagon without apothem

Yes you do not know how much the apothem is worth of the hexagon, you can calculate the area with this other formula:

Area = 2.60 - L2

If you have any questions or have any problems solving an exercise, leave us a comment and we will help you as soon as possible in all matters related to the calculation of the apothem of this six-sided figure or its surface.

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