Octagon is an eight-sided two-dimensional geometrical figure. An octagon is composed of 8 internal angles and also 8 exterior angles. The sum of the inner angles of one octagon is 1080°, and also the amount of the exterior angle is 360°. There are 20 diagonals in one octagon. Octagons room classified into various varieties based upon their sides and also angles. Let united state learn much more about the octagon form in this article.

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 1 What is one Octagon? 2 Types the Octagons 3 Properties of one Octagon 4 FAQs on Octagon

An octagon deserve to be identified as a polygon with eight sides, eight internal angles, and eight vertices. Once all the sides and angles of an octagon room equal in measurement, it is dubbed a continuous octagon. Every polygon is either convex or concave. Convex octagons bulge outwards, whereas concave octagons have indentations (a deep recess). Convex octagons are those in which every the angles suggest outwards. A continual octagon is an instance of a convex octagon. The octagon in i beg your pardon at the very least one of its angles points inwards is a concave octagon. ## Octagon Sides

An octagon is a polygon v 8 sides and 8 internal angles. Words 'Octagon' is obtained from the Greek word, 'oktágōnon' which way eight angles. The is the factor why that is referred to as an octagon.

## Types the Octagons

Depending upon the sides and also angles, an octagon is classified right into the following categories:

Regular and also Irregular OctagonConcave and Convex Octagon

### Regular Octagon

The octagon having eight congruent sides and also angles is well-known as a continual octagon. A constant octagon has all the angle of same measure.

In a constant octagon, all the sides are equal in length, and all the angles space equal in measure.The internal angles include up come 1080° and also the exterior angles include up come 360°.The internal angle at every vertex the a continuous octagon is 135°. ### Irregular Octagon

An octagon in i beg your pardon the sides and also angles space not congruent is an irregular octagon. In other words, an rarely often rare Octagon has eight uneven sides and also eight unequal angles.

It is one octagon with unequal sides and also angles.All the inner angles room of different measure, however their sum is constantly 1080º.

### Convex Octagon

The octagon, which has all its angles pointing outside and no edge pointing inwards, is convex. Each angle the a convex octagon is much less than 180°.

Convex octagons bulge outwards.None the their interior angles is better than 180°. ### Concave Octagon

The octagon in which one of the angle points inward is a concave octagon.

Concave octagons have indentations (a deep recess).The inner angles are better than 180°, the is, at the very least one angle is a reflex angle.

## Properties of an Octagon

Here room a few properties of one octagon that can assist to identify it easily.

An octagon is a polygon with eight sides and also eight angles.All its inner angles amount up come 1080°6 triangles can be developed in a continual octagon v the assist of diagonals using a common vertex.

## Octagon Diagonals

The diagonal of one octagon is the line segment that connects any type of two non-adjacent vertices. There room 20 diagonals in one octagon. The formula that is supplied to discover the number of diagonals in any type of polygon is, number of diagonals = n(n-3)/2; wherein 'n' to represent the variety of sides that the polygon. In this case, there room 8 sides in an octagon. After ~ substituting the worth of 'n' in the formula, we get, variety of diagonals = n(n-3)/2 = 8(8 - 3)/2 = (8 × 5)/2 = 20. Therefore, there space 20 diagonals in an octagon.

## Angles of one Octagon

In a regular octagon, each internal angle is 135°. The amount of an octagon's internal angles is 1080°, and also the sum of the exterior angles of one octagon is 360°.

Sum of interior angles = 135° × 8 political parties = 1080°Sum the Exterior angles = 45° × 8 political parties = 360°

## Area the Octagon

The area of one octagon is the total room occupied by it. The formula to calculation the area that a continuous octagon is, Area that a constant Octagon = 2a2(1 + √2); where 'a' is any one side size of the octagon. That is to express in square units prefer inches2, cm2, and also so on. For example, if one next of a consistent octagon is 6 units, permit us uncover the area the the octagon. Area of octagon = 2a2(1 + √2), Substituting the worth of 'a', Area of octagon = 2 × (62) × (1 + √2) = 72 × (1 + √2) = 173.8 square units.

In case of an rarely often, rarely octagon, over there is no particular formula to discover its area. We divide the octagon into smaller numbers like triangles. Then, after calculating the area of every the triangles, we add their areas to gain the area of the octagon.

## Perimeter of an Octagon

The perimeter the a polygon is the full length the its boundary. In order to calculation the perimeter of an octagon, the size of all the sides must be known. We know that in a regular octagon, all the sides are of same length. Therefore, the formula the is used to uncover its perimeter is,

Perimeter of one octagon = sum of every its sides

Perimeter that a regular octagon = 8a (Where 'a' is the length of one side of the octagon)

Important Notes

An octagon has eight sides.The sum of all the inner angles in one octagon is constantly 1080º.The amount of all the exterior angle in an octagon is constantly 360º.A continual octagon has actually 20 diagonals.Regular octagons are always convex octagons, if irregular octagons deserve to either it is in concave or convex.

Challenging Questions

What is the amount of the variety of sides, vertices, and angles in an irregular octagon?a) 10 b) 8 c) 30 d) 40What is the variety of triangles that have the right to be attracted in a regular octagon by connecting every the vertices?

☛ connected Articles

Example 1: How countless triangles have the right to be developed by joining the vertices of an octagon?

Solution:

In a continual octagon, by involvement one vertex to the continuing to be vertices, 6 triangles have the right to be formed. However, if we consider all the vertices independently, we would have a total of 632 triangles.

Example 3: find the area that a constant octagon if the side procedures 5 units.

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Solution:

The political parties of a continual octagon are of same length. Here, the side length, a = 5 units. We can uncover the area that the octagon using the formula, Area the a constant Octagon = 2a2(1 + √2). Substituting the value of 'a' in the formula, us get, Area that a constant Octagon = 2a2(1 + √2) = 2 × (5)2 × (1 + √2) = 50 × (1 + √2) = 120.71 square units. Therefore, the area that the octagon is 120.71 square units.