Area Formula For A Octagon

Expanse of an octagon is the region covered by an octagon in a two-dimensional aeroplane. An octagon is a two-dimensional geometrical airplane figure. In Geometry, we take studied different types of polygon shapes such as triangle, square, pentagon, hexagon, rectangle, etc. Like other shapes, the octagon is also a polygon.

Octagon has 8 sides and 8 angles. It ways the number of vertices and edges are 8. All the sides of the octagon joined with each other end-to-end to form a shape. These sides are in a straight line segment. They are non curved or disjoint with each other.

Octagon

Area of an Octagon Formula

The area of an octagon is divers as the total space occupied inside the boundary of an octagon. The measurement unit for the area is square units.

If a polygon is with 8 equal sides and eight equal angles, then the polygon is a regular octagon. Otherwise, the polygon is known every bit an irregular polygon.

Area of an Octagon

In the above figure, y'all can meet the figure of a regular octagon, which is divided into eight equivalent triangles. The distance of each vertex from the centre is equal. Here, 'a' shows the length of the sides.

The area of an octagon formula is given as,

Expanse of a regular octagon, A = 2a^two (ane+√ ii ) Square units.

Where "a" is the length of the octagon sides.

Information technology is non possible to find the area of an irregular octagon using this formula. So, to find its area, information technology is divided into other regular polygons. And then, the areas of all polygons should be added to become its expanse.

Area of an Octagon Examples

Question1: Detect the area of regular octagon whose side is 5cm.

Solution:

Given:

Side, a = 5cm

We know that,

Surface area of a regular octagon, A = 2a^two (i+√ 2 ) Square units

A = 2(5)^two (one+√ two ) cm^two

A = ii(25) (1+√ ii ) cm²

A = fifty (i+√ 2 ) cm²

A = 50(one+ane.414) cm²

A = 50(2.414) cm²

A = 120.7 cm²

Therefore, the surface area of a regular octagon is 120.7 cm².

Area of Irregular Octagon

Finding the area of a regular octagon is an easy task because you have been provided past a symmetric figure. A regular octagon has all its sides equal in length. Only in the case of the irregular octagon, the sides accept different dimensions and each angle could be unlike. Therefore, we have alternative methods to discover the area. Hence, here we are providing some important steps to find the surface area of an irregular octagon.

Break the given octagon into triangles.
Find the area of the individual triangle
Add all the areas to get the result.

Let united states of america understand the above steps with the help of an example.

Question 2:

Find the area of an irregular octagon given below:

Area of an irregular octagon

Solution:

The given effigy is an irregular octagon.

Therefore, the area of an irregular octagon ABCDEFGH is given beneath:

Surface area of ABCDEFGH = Area of ABC + Surface area of ACD + Area of ADE +Area of ADE + Area of AFG + Area of AGH

Finding the area of ABC:

Using Heron's Formula:

Southward = (3+6+8)/2

Southward = eight.5

Therefore, the area of ABC =

\(\begin{array}{l}\sqrt{South(S-a)(Due south-b)(Due south-c)}\end{array} \)

\(\begin{array}{l}A =\sqrt{viii.5(8.5-iii)(8.5-6)(eight.five-8)}=vii.64\finish{array} \)

Therefore, the expanse of ABC = vii.64

Similarly, nosotros can observe the area of other triangles using Heron'south formula,

Expanse of ACD = xi.83

Area of ADE = xiv.fourteen

Area of ADE = xi. 39

Area of AFG = 27.81

Surface area of AGH = 35.99

Now, add together all the areas of the triangle

Area of ABCDEFGH = 7.64 + eleven.83 + 14.14 + 11. 39 + 27.81 + 35.99 = 108.83

Hence, the area of an irregular octagon is 108.83 square units

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