**Octagon: **In geometry, the octagon is a polygon that has 8 sides and 8 angles. This means octagon has 8 vertices and edges. 8 straight lines which are joined together from end to end makes an Octagon. On this page we will provide you with all the information on Octogon meaning, definition, shapes, sides, formula etc., Read on to find out more.

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## What Is Octagon In Math?

**Octagon Definition: **Any polygon which has 8 sides and 8 angles is known as Octagon in Geometry.

**Octagon Meaning:** The word Oct means 8 and gon means sides. Together it is known as an Octagon which is nothing but a polygon made of 8 sides.

### Octagon Shape

Octagon belongs to the Polygon family. As we know there are many polygons in geometry such as Triangle, Square, Rectangle, Pentagon, Hexagon etc., similarly, Octagon belongs to the Polygon and the only thing we can differentiate the Octagon shape from other polygons is that Octagon has 8 sides.

A geometrical shape in a two-dimensional plane makes an Octagon. Eight straight lines that are connected from one end to another end make an Octagon. The shape of the Octagon is given below:

In the above image, we can see that the shape of the Octagon can be seen in the top view of an umbrella and in the traffic signals stop signboard.

### Octagon Diagonals

There are 20 diagonals in an octagon and those 20 diagonals in Octagon are shown below:

### Types Of Octagon

Depending upon the Octagon sides and angles, we can classify the Octagons into two categories:

- Regular and Irregular Octagon
- Concave and Convex Octagon

### Regular And Irregular Octagon

An octagon whose sides and angles are equal is known as a regular octagon. An Octagon whose sides and angles are unequal is known as an irregular octagon. Refer to the image below to know what is a regular and irregular octagon.

### Concave And Convex Octagon

An octagon, whose angles are pointing outwards is known as a convex octagon. The angles of the convex octagon will not be more than 180 degrees. Whereas concave octagon is the octagon whose one of the angles is pointing inwards.

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### Properties Of Octagon

- In the above given octagon, ∠A + ∠B + ∠C + ∠D + ∠E + ∠F + ∠G + ∠H = 1080°. In regular octagon, sum on interior angles of an octagon is 1080°, where each angle is equal to 135°(that means 135×8 = 1080).
- The sum of exterior angles of an octagon is 360°. Each exterior angle measure 45° which means 45×8 = 135.
- When it comes to the irregular octagon, all the interior angles will not be equal to 135°, but the sum of the interior angles will be equal to 1080°.
- An octagon has 8 sides and 8 angles.
- All the sides and angles are equal in a regular octagon.
- Approximately 20 diagonals are there in the regular octagon.

### Octagon Formulas

The octagon formulas are given below:

1. Area of Regular Octagon = 2a^{2}(1+√2) 2. The perimeter of Octagon = Sum of all Sides = 8a (a denotes length of the sides of the octagon) 3. Length of the Diagonal of Octagon = L = a√(4 + 2√2) |

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### Octagon Questions

** Q1. Find the perimeter regular octagon whose side is 7 cm? **The side of the Octagon is 7cm.

Answer:

Using the perimeter formula of a regular octagon =

**8a**

**(a denotes length of the sides of the octagon)**

= 8 (7)

= 56 cm.

The perimeter of a regular octagon is 56 cm.

** Q2. find the area of a regular octagon whose side is 5cm?** The area of a regular octagon is

Answer:

**=**2a

^{2}(1+√2)

= 2(5)

^{2}(1+√2)

= 2 (25) (1+√2)

= 120.71 sq.cm

The area of a regular octagon is 120.71 sq. cm whose side is 5cm.

** Q3.Find the length of the longest diagonal of a regular octagon whose side length is equal to 11cm**Length of the Diagonal of Octagon = L = a√(4 + 2√2)

Answer:

= 11√(4 + 2√2)

= 11 √(6√2)

= 11 x √(6.828)

= 11 x 2.613

= 28.743

The length of the longest diagonal of a regular octagon whose side length is equal to 11cm is 28.743.

### FAQs On Octagon

The frequently asked questions on Octagon are given below:

In mathematics, 8 sided shape is called an Octagon.Q. What is an 8 sided shape called? A. |

Octagon has four parallel lines.Q. How many parallel lines does an octagon have? A. |

Regular octagon consists of 8 obtuse angles. Q. How many obtuse angles does a regular octagon have?A. |

A regular octagon has all its sides equal.Q. A regular octagon has all its sides___ A. |

The sum of angles in a regular octagon is equal to 1080 degrees. Q. What is the angle sum of a regular octagon?A. |

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