Hexagon Calculator | 6 - Sided Polygon

We will now take a look at how to find the area of a hexagon using different tricks. The easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. For those who want to know how to do this by hand, we will explain how to find the area of a regular hexagon with and without the hexagon area formula. The formula for the area of a polygon is always the same no matter how many sides it has as long as it is a regular polygon:

• area = apothem × perimeter / 2

Just as a reminder, the apothem is the distance between the midpoint of any side and the center. You can view it as the height of the equilateral triangle formed by taking one side and two radii of the hexagon (each of the colored areas in the image above). Alternatively, one can also think about the apothem as the distance between the center, and any side of the hexagon since the Euclidean distance is defined using a perpendicular line.

If you don't remember the formula, you can always think about the 6-sided polygon as a collection of 6 triangles. For the regular hexagon, these triangles are equilateral triangles. This fact makes it much easier to calculate their area than if they were isosceles triangles or even 45 45 90 triangles as in the case of a square.

For the regular triangle, all sides are of the same length, which is the length of the side of the hexagon they form. We will call this a. And the height of a triangle will be h = √3/2 × a, which is the exact value of the apothem in this case. We remind you that √ means square root. Using this, we can start with the maths:

• A₀ = a × h / 2
• = a × √3/2 × a / 2
• = √3/4 × a²

Where A₀ means the area of each of the equilateral triangles in which we have divided the hexagon. After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula:

• A = 6 × A₀ = 6 × √3/4 × a²

• A = 3 × √3/2 × a²

• = (√3/2 × a) × (6 × a) /2

• = apothem × perimeter /2

We hope you can see how we arrive at the same hexagon area formula we mentioned before.

If you want to get exotic, you can play around with other different shapes. For example, suppose you divide the hexagon in half (from vertex to vertex). In that case, you get two trapezoids, and you can calculate the area of the hexagon as the sum of them. You could also combine two adjacent triangles to construct a total of 3 different rhombuses and calculate the area of each separately. You can even decompose the hexagon in one big rectangle (using the short diagonals) and 2 isosceles triangles!

Feel free to play around with different shapes and calculators to see what other tricks you can come up with. Try to use only right triangles or maybe even special right triangles to calculate the area of a hexagon!