Hello and also welcome to the octagon calculator, the ultimate device for everything octangular. Here, us hope friend will uncover a an excellent tool because that calculating the diagonals, perimeter, circumradius, inradius, and area the a continual octagon. In this octagon area calculator, friend will also find the answers to the adhering to questions: what is an octagon, how countless sides go an octagon have, exactly how to discover the area the a continual octagon or how to draw an octagon.

You are watching: How to find the perimeter of a octagon

We will evaluation the octagon definition, discuss the octagon angles and also how they impact the octagon shape. On height of all that, us will view a few examples that real-world octagons consisting of octagon tiles, flooring, and also the famous "Octagon house"".

Octagon definition: How numerous sides does an octagon have?

The standard definition of an octagon is something along the present of: "An octagon is a polygon through 8 sides delimiting a close up door area". Anyone v a simple understanding the Greek should have the ability to easily price the inquiry how plenty of sides does an octagon have without any type of notions the mathematics. That is because "Octo-" in Greek means eight, so the is safe to assume an octagon has actually eight sides, or that an octopus has actually eight legs.


We will certainly dive a little bit deeper right into the Greek beginning of the octagon shape when we talk around octagon angles, but, because that now, let's stick to octagon sides. If someone asks "how many sides go an octagon have?" the price is always the same, but if castle ask about the length of those sides, there is no one price we deserve to give. Every side of an octagon have the right to have different lengths and still it is in an octagon; there are no limitations on that front. However, when all of an octagons internal angles and side lengths room the same, the is referred to as a regular octagon and also has distinct properties together we will view in the complying with sections.

Octagon angles: What is an octagon?

If us look at the beginning of words "Octagon" it originates from the Greek meaning "eight angles". The an outcome of this is a polygon composed the eight vertices joined by eight directly lines. The eight sides space a necessary an effect of having eight angles. In fact, the typical octagon definition defines the octagon as having eight sides quite than eight angles, however you currently know the both meanings are basically the same. For this reason the concern what is one octagon? is equally fine answered by saying "an eight-sided polygon" as well as "a polygon with eight angles".

While the political parties of an octagon deserve to have virtually any length, the octagon angles room restricted. Over there is not a restriction implemented on every of the angles yet on the sum of them. This is a geometric restriction since it would certainly be impossible to sign up with all eight sides together without complying with this rule. For any kind of octagons, the amount of every one of its internal angles is always 1080°.

This method that a constant octagon will have internal octagon angle of exactly 1080°/8 = 135° (if girlfriend prefer various other units, feel cost-free to usage our edge converter). In our opinion, a constant octagon is lot prettier 보다 all other octagons. Afterwards in the text, we'll see just how to find the area of an octagon and the tricks connected with a consistent octagon.

Area of an octagon: how to discover the area the a continuous octagon?

If you desire to know exactly how to uncover the area the a regular octagon by hand, the simplest procedure is to use the conventional formula for the area that a constant polygon. The formula is the following:

area of continuous polygon = perimeter * apothem / 2,

where the apothem is the street for the facility of the polygon come the mid-point that a side. The perimeter can be calculation a couple of ways: through summing up the size of each side, multiplying the length of one next by the number of sides, or, if you're feeling lazy, friend can additionally use ours perimeter that a polygon calculator.


A trick come remember this formula is to recognize where it come from. If girlfriend look in ~ the apothem you have the right to see that it's the elevation of a triangle make by taking a heat from the vertices the the polygon/octagon to the center of it. The resulting triangle is what is referred to as an isosceles triangle and its area is:

area the triangle = base * height / 2

as we explained in the triangle area calculator. Keep in mind that the basic of the triangle is the size of a side of the octagon. Due to the fact that there are as countless of this triangles together the polygon has sides (eight for an octagon), you need to multiply the area the this triangle by the variety of sides. Girlfriend will obtain the full area the the octagon:

area the octagon = 8 * basic * elevation / 2 = perimeter * apothem / 2.

These tricks occupational for any polygon, e.g., hexagons and any other polygon you have the right to think of, as long as that is regular. Personally from making use of triangles, there are other tricks you deserve to use to calculation the area of an octagon if friend don't remember the formula, but they will certainly not occupational for various other polygons. Because that example, if friend imagine an octagon form inside of a square you have the right to see that the distinction is only four right triangles. "How to uncover the area that a continual octagon with this information?" you might ask. Well, the is really easy:

Enjoy success!

Alternatively, you deserve to use this trick. If you organize the right triangles correctly, you can construct a square from all 4 of them. In this case, the hypotenuse is likewise the next of the octagon. Then you have the right to calculate the area of the parallel you just made indigenous the 4 right triangles, and subtract the from the area that the huge square.

On peak of these, you can get even more creative. Because that example, imagine that the octagon is written by a rectangle v two trapezoids, through one over and listed below the rectangle. In this case, it will certainly be much simpler to calculate the area, since you only have to sum up the area the the rectangle plus double the area of one of the trapezoids, due to the fact that both trapezoids are equal.

Diagonals the a constant octagon

In total, an octagon has 20 diagonals; the longest ones space on that is axes of symmetry and they meet at the main point, O, i m sorry is likewise the beginning of symmetry. There are three species of diagonals (take a look at the image above in the "Area of an octagon" ar for reference):

Short diagonals, because that example, AG, FH or CE;Medium diagonals, such together AF or it is in (also called the height of an octagon);Long diagonals, because that example, AE or BF.

You deserve to derive the formula because that each the them with ease using the basic principles that geometry. Here are the formulas because that the size of the diagonals:

Short diagonal s = a * √(2 + √2)Medium diagonal m = a * (1 + √2)Long diagonal l = a * √(4 + 2√2).

If you're emotion lazy or find yourself in a rush, just use the octagon calculator.

Circumradius and also inradius

We should likewise talk around the circumradius and the inradius. Ours octagon area calculator is capable of finding the radii that the circumscribed and inscribed circles.

You can an alert that the circumradius is simply fifty percent of the length of the longest diagonal:

R = l/2 = a / 2 * √(4 + 2√2)

Similarly, the inradius is the exact same as the apothem, i m sorry is just fifty percent of the octagon's height:

r = m/2 = a/2 * (1 + √2)

Octagon shape: how to attract an octagon?

It can seem easy to draw an octagon in ~ first, and, in principle, it is. Simply draw any type of shape v eight directly sides and you're done. However normally, what people want to draw is no any octagon, however a regular octagon, together its is the octagon form that pertains to mind first. So let's see how to attract an octagon as regularly and also as simple as possible.

The most precise way would be to use appropriate drawing tools and also start illustration the constant octagon shape one side at a time, joining them v the corresponding 135° continuous octagon angles. But not everyone has actually such tools laying about so that is not a very practical method. To achieve the octagon shape we room looking for, it is ideal to start with that is circumference, because it can be attracted by hand (not recommended) or by utilizing a glass, cup or even a coin.

With the circumference drawn, start dividing the corresponding circle area right into halves. First, you will make two half-circles. Then, divide them in fifty percent again and also get four quarter circles. Halve the once more and you end up v **eight circle-eights**. We can now take the point out of division along the circumference and also join the surrounding ones with a straight line. The an outcome is a perfectly constant octagon, minus the human being error you may make whilst drawing and also halving.Another just how to attract an octagon trick would be the one us have already discussed as soon as learning just how to discover the area of one octagon through squares. Start by drawing a large square and then 'chop off' the corners. The math term because that this procedure is truncating the square. If you execute it right, friend will acquire a constant octagon form out that it. This an approach is no as an accurate as the ahead one, yet it's much easier to perform without any type of tools at all.

How to usage the octagon calculator

Using the octagon calculator is also complicated, yet just in case someone can have any kind of doubts and for the services of completeness, let's go over the features and also uses the this octagon area calculator. First of all, we need to look in ~ the different fields and what castle mean.

Side length - the is the size of every side of the continuous octagon.Perimeter - sum of the size of all the sides of the octagonArea - room enclosed by the octagon itselfLongest diagonal line - size of the heat joining 2 furthest verticesMedium diagonal line - length of the heat joining 2 vertices v 3 vertices in between themShortest diagonal line - length of the heat joining 2 vertices with 2 vertices in in between themCircumcircle radius - Radius the the one that has all 8 vertices that the continuous octagonIncircle radius - Radius of the smallest circumference the is tangent to all 8 sides

Now the you understand what every of the parameters means, that is time to see how to use the octagon calculator come easily obtain the worths you space looking for. The finest feature that this calculator is the it just requires one input to calculation the rest of the values. This is what provides the octagon calculator the fastest means to calculate any properties of one octagon, by a far-ranging margin.

Octagons in real life: the octagon house

So much we have actually talked about the octagon an interpretation and exactly how to attract an octagon. We've seen photos of octagons and even answer the (now obvious) question of how many sides walk an octagon have. Now, that is time to see how octagons are supplied in real life. The octagon shape is less complicated to manufacture and also use in designs 보다 a circle, because of the level sides and the octagon angles. We can often discover octagon tiles together flooring or in a bathroom. There space even dwellings that have actually an octagon shape, many notably the famed "Octagon House".

The Octagon house is a house developed in an octagonal form in Washington D.C. In the USA. That was constructed for Colonel john Tayloe III. This is the reason, it's likewise known as Colonel man Tayloe III House. It adheres to the American "tradition" of naming structures after their shape, together they did v the Pentagon. The Pentagon is the headquarters of the United says Department that Defence and was built in the shape of a consistent pentagon.

The Octagon home has plenty of interesting architectural attributes such a triangular business stairway, a enlarge oval stairway and the evident octagonal shape of the building. On height of such unique characteristics, there are numerous ghost stories neighboring the house, partly because the owner was an essential figure in the at an early stage American history.

More real-world provides of Octagons: Octagon tiles and camera apertures

Like any kind of regular polygon, the octagon form turns out to be useful in numerous different applications. Us have already talked about making residences in an octagonal form and, sticking v buildings, octagons are specifically popular as soon as it pertains to flooring, mainly in the type of octagon tiles. The form of a constant octagon method that us can integrate octagon tiles and square tiles to totally fill the floor of any room, no issue its square footage. Utilizing a various pattern in each type of tile, or through using various colors, this combinations would permit you to produce a beautiful floor for your kitchen or bathroom. Just remember to use our brick calculator to assist you!

Another amazing use the octagons is within photographic cameras. In particular, the shutter the protects the sensor native exposure come light as soon as the camera is not in use. This shutter, or aperture, is constantly made following a regular polygonal shape, consisting of the octagon shape. You can learn more about aperture and how to play with it come get more professional looking pictures with our aperture area calculator.

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Before girlfriend head the end to check that calculator we desire to give you a quick tip/trick. Once you see a snapshot of a bright source of light, you can have noticed the it looks favor a star with a different variety of pointy arm, depending upon the camera. This is the an essential to figure out if your camera has an octagon aperture or not: the number of pointy eight is exactly equal come the number of political parties of the polygon that renders up the aperture. And how plenty of sides go an octagon have? Exactly! So you only need to look because that 'star shapes' through 8 pointy arms and also you'll know that this picture was taken making use of an octagonal aperture. It functions every time - it's physics, and, much more specifically, a diffraction pattern.