Octagon is an eight-sided two-dimensional geometrical figure acquired fromGreek native "octa," which supposed "eight," and "gonon" which meant "angles. There room 20 diagonals in an octagon. One octagon consists of 8 internal angles and 8 exterior angles. The amount of one octagon's internal angles is 1080°, and also the sum of the exterior angle of an octagon is 360°. Octagons space classified into various types based upon your sides and angles. Let's learn much more about the octagon shape in this article.

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 1 What is one Octagon? 2 Shape the Octagon 3 Types of Octagons 4 Properties of an Octagon 5 Angles of one Octagon 6 Perimeter of an Octagon 7 Solved examples on Octagon 8 Practice concerns on Octagon 9 FAQs top top Octagon

## What is one Octagon?

An octagoncan be defined as a polygonhaving eight sides joined together with one another, eight interior angles, and also eight vertices. As soon as all the sides and also angles of one octagon are equal in measurement, that is referred to as a consistent octagon, while once it contends least two sides or angles in various measurements, the is known as an irregular octagon. Every polygon is one of two people convexor concave. Convexoctagons bulge outwards, conversely, concaveoctagons have actually indentations (a deep recess). Convex octagons room those in which every the angles point outwards. A consistent octagon is an instance of a convex octagon.The octagon in i m sorry at the very least one that its angle pointinwards is a concave-shaped octagon.

## Shape the Octagon

Anoctagon have the right to be taken into consideration asa one attempting to come to be a squareora square attempting to end up being a circle. Octagon is a geometrical shape in a 2D plane. Octagons havestraight sides the connect; they probably curved yet connected.An octagon has 8 right sides. The shape must additionally be closed. Among the most popular examples of the octagon is the protect against signboard. ## Octagon Sides

An octagon has 8 sides and also 8 inner angles. The word 'Octagon" is derived from the Greek word, 'oktágōnon' which way eight angles. That is the reason why that is referred to as an octagon.

## Types the Octagons

Depending ~ above the sides and also angles in anoctagon, the is classified right into the following categories:

Regular and also Irregular OctagonConcave and Convex Octagon

### Regular Octagon

The octagon having actually eight congruent sides and angles is recognized as a constant octagon. Every constant octagon has the very same angle measures.

All sides room equal in length, and also all the angles room equal in measure.The interior angles include up come 1080°(135x8)and the exterior angles add up to 360°.The inner angle at each vertex of a continual octagon is 135°.The central angle is 45°. ### Irregular Octagon

Anoctagon that does not have any type of congruent sides or congruentanglesis an rarely often, rarely octagon.An irregular Octagon has actually eight unequalsides and eight unlike angles.

It is anoctagon through unequal sides and angles.All the angles are different in measurement, but the amount is always 1080º. ### Convex Octagon

The octagon, which has actually all its angle pointing outside and also noanglepointing inwards, is convex. Every angle that a convex octagon is much less than 180°.

Convexoctagons bulge outward.None the their internal angles is greater than 180° ### Concave Octagon

The octagon in which among the angle pointing inward is a concave-shaped octagon.

Concaveoctagons have indentations (a deep recess).The internal angles are better than 180° ## Properties of an Octagon

Here room a couple of properties of a continuous octagon related to itsangles, sides, and diagonals.

It has actually eight equal sides and also eight equal angles.All its interiorangles amount upto1080°The measure up of its main angles equals45°The variety of trianglesin a consistent octagon the is developed by illustration the diagonals from a given vertex to the continuing to be vertices is 6

## 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 the is used to uncover the number of diagonals in any polygon is, variety of diagonals = n(n-3)/2; whereby 'n' represents the number of sides of the polygon. In this case, there space 8 political parties in one octagon. ~ substituting the value of 'n' in the formula, us get, number 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

We have already discussed the angle of aregular octagon in the section: nature of octagons.In a continual octagon, the vertex's inner angle is 135°, and also the central angle is 45°.The amount of one octagon's internal angles is 1080°, and also the amount of the exterior angles of an octagon is 360°.

Sum of internal angles = 135°× 8 political parties = 1080°Sum that Exterior angle = 45°× 8 sides = 360° ## Area of Octagon

The area of an octagon is the total an are occupied by it. That is calculated with the formula, Area that a constant Octagon = 2a2(1 + √2); where 'a' is any kind of one side length of the octagon. The is expressed in square units favor inches2, cm2, and also so on. Because that example, if one next of a consistent octagon is 6 units, permit us discover the area that the octagon. Area that octagon = 2a2(1 + √2), Substituting the worth of 'a', Area of octagon = 2 × (62)× (1 + √2) = 72 × (1 + √2) = 173.8 square units.

## Perimeter of an Octagon

To calculate the perimeter, the length of all sides must be known. Because that a continual octagon,the length of every sides is the same. Together per the perimeter of the octagon formula, main point 8 with the side size to understand the perimeter value.

The perimeterof a consistent octagon = sum of all its sides = 8a (Where "a"is the size of one side of the octagon) Important Notes

An octagonhas eightsides.The amount of every the internal angles in one octagon is always 1080º.The amount of every the exterior angle in one octagon is constantly 360º.A regular octagonhas 20 diagonals.Regular octagons room alwaysconvex octagons, while irregular octagons caneitherbe concave or convex.

Thinking out of the Box!

Explorea few famous octagonalbuildings and also structures around the world.

Challenging Questions

What is the amount of the number of sides, vertices, and also angles in an irregular octagon?a) 10b) 8c) 30d) 40What is the variety of triangles that deserve to be attracted in a continual octagon through connecting all the vertices?

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Example 1:Lucas is curious to know the numberoftriangles developed by involvement the vertices of one octagon. Let's assist him!

Solution:

In a regularoctagon, by authorized one vertex come the remaining vertices,6triangles have the right to be formed. Similarly, if you space considering every the vertices independently, you will have actually a complete of 632 triangles. Therefore,632 triangles in all.

Example 2: Noah was addressing a Math sum which forced him to calculate thelength of each side that a regularoctagon when the perimeter of theoctagon was provided as 160 units. Let's help him out!

Solution:

According come the consistent octagon definition,all of itssides space of equallength. The perimeter of one octagon = 8 ×(side). Here, the perimeter is provided as 160 units. Thus, the size of every side = 160÷8 = 20 units. Therefore, the size of each side of one octagon who perimeter is 160 units is 20 units.

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Example 3: Alex is planningto build an octagonal-shapedgarden in front of his house. As per his plan, each side the the octagonal garden will certainly measure 10 units. That needsto to buy a fence wire to place roughly the border of the garden. Find the size of the fence cable required.

Solution:

We recognize that the garden is octagonal shaped. Size of the next of the octagonal garden = 10 units. To uncover the size of the fencewire required, we need to discover the garden's perimeter. We currently know thatthe perimeter of an octagon = 8 ×side. Hence, the perimeter the the garden = (10×8) units = 80 units