We can determine the area of a hexagon by i dentifying the length of the side of the hexagon. Always write the final answer of area in square units. The formula to calculate the regular hexagon perimeter is 6a units, where 'a' is the side length of the hexagon. In the case of an irregular hexagon, we add the side lengths.
Learn Practice Download. Hexagon A hexagon is a closed 2D shape that is made up of straight lines. Hexagon Definition 2. Types of Hexagon 3. Properties of a Hexagon 4. Hexagon Formulas 5. Hexagon Examples Example 1: What is the area of a regular hexagon with sides equal to 3 units? Have questions on basic mathematical concepts?
Become a problem-solving champ using logic, not rules. Practice Questions on Hexagon. Explore math program. Explore coding program. Polygons Worksheet. Make your child naturally math minded. Book A Free Class. The sum of interior angles of the four triangles equals the sum of interior angles of the hexagon. A regular hexagon is a hexagon in which all sides have equal length and all interior angles have equal measure.
Sides of a regular hexagon are equal in length and opposite sides are parallel. From the center, a regular hexagon can be divided into six equilateral triangles , each having side length, s, as shown below. The area, T, of one of the equilateral triangles, drawn in blue, can be found by using , where the apothem is the height of the triangle. Since there are six equilateral triangles, the area of a regular hexagon is.
Example: Find the area of a regular hexagon that has a side length of 8. Long diagonals - they always cross the central point of the hexagon. Short diagonals - The do not cross the central point. They are constructed joining two vertices leaving exactly one in between them.
You should be able to check the statement about the long diagonal by visual inspection. However checking the short diagonals take a bit more ingenuity. But don't worry it's not rocket science , and we are sure that you can calculate it yourself with a bit of time; remember that you can always use the help of calculators such as the right triangle side lengths calculator. Another pair of values that are important in a hexagon are the circumradius and the inradius.
The circumradius is the radius of the circumference that contains all the vertices of the regular hexagon. The inradius is the radius of the biggest circle contained entirely within the hexagon. Now we are going to explore a more practical and less mathematical world: how to draw a hexagon. For a random irregular hexagon the answer is simple: draw any 6-sided shape so that it is a closed polygon and you're done.
But for a regular hexagon things are not so easy since we have to make sure all the sides are of the same length. To get the perfect result you will need a drawing compass. Draw a circle, and, with the same radius, start making marks along it. Starting at a random point and then making the next mark using the previous one as the anchor point draw a circle with the compass. You will end up with 6 marks, and if you join them with the straight lines , you will have yourself a regular hexagon.
You can see a similar process on the animation above. The hexagon calculator allows you to calculate several interesting parameters of the 6-sided shape that we usually call a hexagon. Using this calculator is as simple as it can possibly get with only one of the parameters needed to calculate all others, as well as including a built-in length conversion tool for each of them.
We have discussed all the parameters of the calculator, but for the sake of clarity and completeness we will now go over them briefly:.
If you like the simplicity of this calculator we invite you to try our other polygon calculators such as the regular pentagon calculator or even 3-D calculators such as the pyramid calculator , triangular prism calculator , or the rectangular prism calculator. Everyone loves a good real-world application , and hexagons are definitely one of the most used polygons in the world. Starting with human usages, the easiest and probably least interesting use is hexagon tiles for flooring purposes.
The hexagon is an excellent shape because it perfectly fits with one another to cover any desired area. If you're interested in such a use, we recommend the flooring calculator and the square footage calculator as they are very good tools for this purpose. The next case is common to all polygons, but it is still interesting to see.
In photography, the opening of the sensor almost always has a polygonal shape. This part of the camera called the aperture , and dictates many properties and features of the pictures taken by the camera. The most unexpected one is the shape of very bright point-like objects due to the effect called diffraction grating , and it is illustrated in the picture above.
One of the most important uses of hexagons in the modern era, closely related to the one we've talked about in photography, is in astronomy. One of the biggest problems we experience when trying to observe distant stars is how faint they are in the night sky.
That is because despite being very bright objects, they are so very far away that only a tiny fraction of their light reaches us; you can learn more about that in our luminosity calculator. On top of that, due to relativistic effects similar to time dilation and length contraction , their light arrives on the Earth with less energy than it was emitted. This effect is called the red shift. The result is that we get a tiny amount of energy with a bigger wavelength than we would like.
The best way to counteract this, is to build telescopes as big as possible. The problem is that making a one-piece lens or mirror bigger than a couple meters is almost impossible, not to talk about the issues with logistics. The solution is to build a modular mirror using hexagonal tiles like the ones you can see in the pictures above. Making such a big mirrors improves the angular resolution of the telescope as well as the magnification factor due to the geometrical properties of a "Cassegrain telescope".
So we can say that thanks to regular hexagons we can see better, further and more clearly than we could have ever done with only one-piece lenses or mirrors. Did you know that hexagon quilts are also a thing?? The honeycomb pattern is composed of regular hexagons arranged side by side. They completely fill the entire surface they span, so there aren't any holes in between them.
This honeycomb pattern appears not only in honeycombs surprise! In fact, it is so popular that one could say it is the default shape when conflicting forces are at play, and spheres are not possible due to the nature of the problem. From bee 'hives' to rock cracks through organic chemistry even in the build blocks of life: proteins , regular hexagons is the most common polygonal shape that exists in nature.
And there is a reason for that: the hexagon angles.
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