Octagon: Shape, Sides, Angles, Meaning, Formula - Embibe

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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 is 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 a concave octagon is an octagon whose one of the angles is pointing inwards.

Properties

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 = 2a2(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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Solved Questions

Q1. Find the perimeter regular octagon whose side is 7 cm? Answer: The side of the Octagon is 7cm.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?Answer: The area of a regular octagon is = 2a2(1+√2) = 2(5)2(1+√2) = 2 (25) (1+√2) = 120.71 sq.cmThe 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 11cmAnswer: Length of the Diagonal of Octagon = L = a√(4 + 2√2) = 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

The frequently asked questions on Octagon are given below:

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

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

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

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

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

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