How long are the sides of an octagon

This is the angle you need to cut at to make an octagon shape. A 3 - sided shape is called a triangle. Triangles are polygons with three sides, so any polygon with three sides is called a triangle. In geometry, a dodecagon or 12 -gon is any twelve- sided polygon. A polygon is a closed plane figure with three or more sides that are all straight.

The following figure is not a polygon as it is not a closed figure. A circle is not a polygon as it does not have straight sides. In geometry, a heptagon is a seven- sided polygon or 7 -gon. The heptagon is sometimes referred to as the septagon, using "sept-" an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate together with the Greek suffix "-agon" meaning angle.

Octagon Formula. A polygon is a two-dimensional 2-D closed figure made up of straight line segments. In geometry, the octagon is a polygon with 8 sides. If the lengths of all the sides and the measurement of all the angles are equal, the octagon is called a regular octagon.

In geometry, a hexagon from Greek? Answer Expert Verified A convex octagon has no angles pointing inwards. In option 2 you can see that one angle is pointing inward, then this octagon is concave. How do you find the sides of an octagon with diameter? When all these eight sides are equal in length, it is known as a regular octagon, whereas when even at least one of the sides is different in measurement, it is known as an irregular octagon.

No, an octagon is not a quadrilateral. A quadrilateral is a closed shape with four vertices and four sides and an octagon has 8 sides and 8 vertices. All octagons need not have equal sides. Octagons that have equal sides are known as regular octagons, while irregular octagons have different side lengths. An octagon has 20 diagonals in all and the longest ones are on its axes of symmetry, and they meet at the central point, which is also the origin of symmetry.

A regular octagon has 4 pairs of parallel sides. There are a total of 8 sides in an octagon, and those eight sides are parallel to their respective opposite side in the case of a regular octagon. Learn Practice Download. Octagon Octagon is an eight-sided two-dimensional geometrical figure. What is an Octagon? Types of Octagons 3. Properties of an Octagon 4. Octagon Examples Example 1: How many triangles can be formed by joining the vertices of an octagon?

Solution: In a regular octagon, by joining one vertex to the remaining vertices, 6 triangles can be formed. However, if we consider all the vertices independently, we would have a total of triangles. Solution: According to the regular octagon definition, all its sides are of equal length. Example 3: Find the area of a regular octagon if its side measures 5 units.

Solution: The sides of a regular octagon are of equal length. We will dive a bit deeper into the Greek origin of the octagon shape when we talk about octagon angles, but, for now, let's stick to octagon sides. If someone asks "how many sides does an octagon have? Every side of an octagon can have different lengths and still be an octagon; there are no restrictions on that front.

However, when all of an octagons internal angles and side lengths are the same, it is called a regular octagon and has special properties as we will see in the following sections.

If we look at the origin of the word " Octagon " it comes from the Greek meaning " eight angles ". The result of this is a polygon composed of eight vertices joined by eight straight lines. The eight sides are a necessary consequence of having eight angles. In fact, the standard octagon definition defines the octagon as having eight sides rather than eight angles, but you already know that both definitions are virtually the same.

So the question what is an octagon? While the sides of an octagon can have almost any length, the octagon angles are restricted. There is not a restriction imposed on each of the angles but on the sum of them. This is a geometric restriction since it would be impossible to join all eight sides together without following this rule.

In our opinion, a regular octagon is much prettier than all other octagons. Later on in the text, we'll see how to find the area of an octagon and the tricks associated with a regular octagon. If you want to know how to find the area of a regular octagon by hand, the easiest procedure is to apply the standard formula for the area of a regular polygon. The formula is the following:. The perimeter can be calculated a few ways: by summing up the length of each side, multiplying the length of one side by the number of sides, or, if you're feeling lazy, you can also use our perimeter of a polygon calculator.

A trick to remember this formula is to understand where it comes from. The resulting triangle is what is called an isosceles triangle and its area is:.

Note that the base of the triangle is the length of a side of the octagon. Since there are as many of these triangles as the polygon has sides eight for an octagon , you have to multiply the area of this triangle by the number of sides.

You will obtain the total area of the octagon:. These tricks work for any polygon, e. Apart from using triangles, there are other tricks you can use to calculate the area of an octagon if you don't remember the formula, but they will not work for other polygons.

For example, if you imagine an octagon shape inside of a square you can see that the difference is only four right triangles. Well, it is very easy:. Alternatively, you can use this trick.

If you organize the right triangles correctly, you can construct a square from all four of them. In this case, the hypotenuse is also the side of the octagon. Then you can calculate the area of the parallelogram you just made from the four right triangles, and subtract it from the area of the big square.

On top of these, you can get even more creative. For example, imagine that the octagon is composed by a rectangle with two trapezoids, with one above and below the rectangle. How to Convert Circumference to Diameter on a Calculator. How to Find the Number of Sides of a Polygon. How to Calculate the Apothem of a Polygon.

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