And there is a reason for that: the hexagon angles. Try to use only right triangles or maybe even special right triangles to calculate the area of a hexagon!įrom bee 'hives' to rock cracks through organic chemistry (even in the build blocks of life: proteins), regular hexagons are the most common polygonal shape that exists in nature.
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You can even decompose the hexagon in one big rectangle (using the short diagonals) and 2 isosceles triangles!įeel free to play around with different shapes and calculators to see what other tricks you can come up with. You could also combine two adjacent triangles to construct a total of 3 different rhombuses and calculate the area of each separately. In that case, you get two trapezoids, and you can calculate the area of the hexagon as the sum of them. For example, suppose you divide the hexagon in half (from vertex to vertex). If you want to get exotic, you can play around with other different shapes. We hope you can see how we arrive at the same hexagon area formula we mentioned before. After multiplying this area by six (because we have 6 triangles), we get the hexagon area formula: Where A₀ means the area of each of the equilateral triangles in which we have divided the hexagon. And the height of a triangle will be h = √3/2 × a, which is the exact value of the apothem in this case. 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 an octagon.įor the regular triangle, all sides are of the same length, which is the length of the side of the hexagon they form. For the regular hexagon, these triangles are equilateral triangles. If you don't remember the formula, you can always think about the 6-sided polygon as a collection of 6 triangles. 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.
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).
Just as a reminder, the apothem is the distance between the midpoint of any side and the center. 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:
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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 easiest way is to use our hexagon calculator, which includes a built-in area conversion tool. We will now have a look at how to find the area of a hexagon using different tricks. It will also be helpful when we explain how to find the area of a regular hexagon. This fact proves to be of the utmost importance when we talk about the popularity of the hexagon shape in nature. Where side refers to the length of any one side.Īs for the angles, a regular hexagon requires that all angles are equal and sum up to 720º, which means that each individual angle must be 120º. These restrictions mean that, for a regular hexagon, calculating the perimeter is so easy that you don't even need to use the perimeter of a polygon calculator if you know a bit of math. For the sides, any value is accepted as long as they are all the same. In a regular hexagon, however, all the hexagon sides and angles must have the same value. The angles of an arbitrary hexagon can have any value, but they all must sum up to 720º (you can easily convert them to other units using our angle conversion calculator). In very much the same way an octagon is defined as having 8 angles, a hexagonal shape is technically defined as having 6 angles, which conversely means that (as you can see in the picture above) the hexagonal shape is always a 6-sided shape.
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