Octagon is a polygon in geometry, which has 8 sides and also 8 angles. That means the number of vertices is 8 and the variety of edges is 8. In an easy words, octagon is a 8-sided polygon and it is a 2 dimensional airplane figure. All the sides space joined v each other end-to-end to type a shape. These sides room in a right line form; they space not bent or disjoint with each other. Each interior angle that a constant octagon is 135°. Therefore, the measure up of exterior angle becomes 180° – 135° = 45°. The amount of the internal angles the the octagon is 135 × 8 = 1080°. In this article, let us talk about the octagon shape, that is formulas, properties, and also examples in detail.

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Table of Contents:

Shape the Octagon

Octagon is a geometrical shape in a two-dimensional plane. Favor the various other polygon shapes, i m sorry we have studied in geometry, such together triangle, square, pentagon, hexagon, rectangle, etc., the octagon is likewise a polygon. The points which specify it various from various other geometrical shapes is that it has actually 8 sides and 8 angles.

If squares are built internally or externally on every the political parties of one octagon, climate the midpoints that the sections joining the centres of the opposite squares form a quadrilateral: equi-diagonal and orthodiagonal ( who diagonals size are equal and also they bisect each various other at 90 degrees).

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You deserve to see in the above figure, there room 8 sides of the polygon and eight vertices together well. This is a regular octagon due to the fact that all the angles and also sides right here are equal. In the same way, based upon sides and also angles, there are many species of polygons, such as:

TriangleQuadrilateralPentagonHexagonheptagonNonagonDecagon, and so on.

Octagon form Images

We can have it was observed that various objects the we use in our day-to-day life save an octagonal shape. Several of the examples incorporate the following:

Outline of an umbrella through 8 ribsStop authorize board in ~ the signalsA wall surface clock through 8 edges

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Octagon sides

In the vault section, you learned around the form of an octagon v the help of one image. Let’s know octagon sides and how to represent them.

How countless sides walk an octagon have?

As we currently know, octagon os a 8-sided polygon. That means, an octagon has 8 sides. Also, based upon the length of this sides, octagons room classified as regular and also irregular octagons.

Octagon angles

As identified above, the octagonal shape has 8 angle at 8 vertices. Thus, the octagon hold 8 sides and 8 angles. There are 8 inner angles and 8 exterior angles in an octagon. Octagon internal angles amount is same to 1080 degrees. Also, the sum of every the eight exterior angle is equal to 360 degrees. Based on the kind of angles, octagons room classified together convex and also concave octagons.

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Types that Octagon

Depending ~ above the sides and angles of the octagon, it is classified right into the complying with categories;

Regular and also Irregular OctagonConcave and also Convex Octagon

Regular and Irregular Octagon

When one octagon has actually all same sides and also equal angles, then it is defined as a regular octagon. But if it has actually unequal sides and also unequal angles, it is characterized as an rarely often, rarely octagon. Check out the figure listed below to watch the difference in between them.

A constant octagon is a closed form with political parties of equal length and interior angle of the exact same measurement. It has eight symmetric lines and rotational equilibrium of order 8. The inner angle at every vertex of a continuous octagon is 135°. The main angle is 45°.

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In the above figure, the left-hand side figure depicts a consistent octagon and also the two figures on the appropriate side reflects irregular octagons. Indigenous the figure itself, we can analyse that there is a difference between the the contrary of regular and irregular polygons.

Convex and also Concave Octagon

The octagon which has actually all its angle pointing exterior or no angles pointing inwards, is a convex octagon. The angles of the convex octagon are not an ext than 180°. And also the octagon, with among its angle pointing inward, is a concave-shaped octagon.

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In the above figure, you have the right to see, the convex octagon has all its angles pointing external from the center or origin point. Conversely, on the appropriate side, the concave octagon has actually one that the angle pointing

towards the inside of the polygon.

Octagon diagonals

For any type of n-sided polygon, we can find the variety of diagonals making use of the formula n(n – 3)/2.

Similarly, us can uncover the variety of diagonals in one octagon.

For octagon, n = 8

Substituting n – 8 in the required formula, we get;

n(n – 3)/2 = 8(8 – 3)/2 = 4(5) = 20

Therefore, an octagon has a complete of 20 diagonals. These have the right to be drawn as presented in the listed below figure.

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Length the the diagonal line of Octagon

If we sign up with the the contrary vertices of a continuous octagon, climate the diagonals developed have the length equal to:

L = a√(4 + 2√2)

where a is the side of the octagon.

Perimeter of Octagon

The perimeter the the octagon is the size of the sides or borders of the octagon, which forms a closeup of the door shape.

Therefore,

Perimeter = amount of all Sides = 8a

Where a is the size of one side of the octagon.

Area of continual Octagon

Area that the octagon is the region covered by the sides of the octagon. The formula because that the area that a regular octagon which has 8 equal sides and all its interior angles room equal to 135°, is provided by:

Area = 2a2(1 + √2)This is the octagon area formula incase of equal sides.

Properties of Octagon

In the instance of properties, us usually take into consideration regular octagons.

These have actually eight sides and also eight angles.All the sides and also all the angles are equal, respectively.There space a total of 20 diagonals in a constant octagon.The complete sum that the interior angles is 1080°, wherein each angle is same to 135°(135×8 = 1080)Sum of all the exterior angles of the octagon is 360°, and also each angle is 45°(45×8=360).

Octagon currently of symmetry

We understand that the heat of the opposite of a form divides that into similar halves. Thus, being an 8 face polygon, it has 8 lines of symmetry. However, these lines the symmetry can be drawn for constant octagons and also this can be presented as:

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Octagonal Prism

A prism may contain at most octagonal faces and also this is known as an octagonal prism. The shape of an octagonal prism is given as:

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Octagonal Pyramid

If the basic of a pyramid is an octagon, then we call it an octagonal pyramid. The form of an octagonal pyramid is given in the figure below.

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Octagon Examples

Q.1: If the length of the next of a regular octagon is 5 cm. Find its perimeter and area.

Solution:

Given, a = 5 cm

Therefore, Perimeter = 8a = 8 × 5 = 40 cm

And Area = 2a2(1+√2) = 2 × 52 (1+√2) = 2 × 25 (1+√2)= 120.7 cm2

Q.2: If the side length of a continuous octagon is 7 cm. Find its area.

Solution:

Given, length of the side of the octagon, a = 7 cm

Area = 2a2(1+√2) = 2 (7)2(1+√2) = 236.6 sq.cm.

Q.3: find the size of the longest diagonal of a consistent octagon who side length is equal to 10 cm.

Solution:

Given,

Length of next of octagon = a = 10 cm

By the formula, us know, the length of the longest diagonal line formula is given by:

L = a√(4 + 2√2)

Hence,

L = 10√(4 + 2√2)

L = 10 x √6.828

L= 10 x 2.613

L = 26.13 cm

Q.4: uncover the area and perimeter that a continuous octagon whose side is of size 2.5 cm.

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Solution:

Given,

Length of side of octagon = a = 2.5 cm

Area that octagon = 2a2(1+√2)

A = 2 x (2.5)2 (1+√2)

A = 12.5 x (1+√2)

A = 30.177 sq.cm

Perimeter that Octagon = 8 x sides of the octagon

P = 8 x 2.5

P = 20cm
In geometry, an octagon is a polygon that has 8 sides and 8 angles. All the sides space joined end to finish to kind the form of the octagon. The sum of the interior angles of one octagon is equal to 1080 degrees.