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Area of an Octagon Formula | How to Calculate Regular Octagon? Examples

Area of an Octagon

Area of an Octagon is the amount of space occupied by the octagon which is basically a polygon with 8 sides. Candidates can check How to Calculate Regular Octagon? Below given solved Examples will show you the correct way of using Area of an Octagon Formula.

A regular octagon has equal sides and internal angles and the internal angle in any vertex of a regular polygon is 135o. The exterior angles measure 45 degrees each, candidates are advised to check below shaped image.

Area of an Octagon Formula

Where ‘A’ Is The Length Of Any One Side Of The Octagon

Properties of Regular Octagon:

Before using the octagon formula, candidates are advised to have a look on some some basic properties of a regular octagon from below:

  • It has 8 sides and 8 interior angles.
  • All the sides are equal in length and all the angles are equal in measurement.
  • There are a total of 20 diagonals in a regular octagon.
  • Each interior angle measures 135 degrees. Hence, the sum of all interior angles is (135 x 8) 1080 degrees.
  • Each exterior angle measures 45 degrees. Hence, the sum of all exterior angles is (45 x 8) 360 degrees.

How to Find: Area of Parallelogram

Area of an Octagon

Solved Examples

Question: Find the area of an octagon of side 9 cm ?

Solution:

Given,
Side of an octagon = a = 9 cm

Area of an octagon
= 2 ×× a2 ×× (1 + 2–√2)
= 2 ×× 92 ×× (1 + 2–√2) cm2
= 2 ×× 81 ×× (1 + 1.414) cm2
= 391.103 cm2

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Question: Find the area of an octagon of side 17 cm ?

Solution:

Given,
Side of an octagon = a = 17 cm

Area of an octagon
= 2 ×× a2 ×× (1 + 2–√2)
= 2 ×× 172 ×× (1 + 2–√2) cm2
= 2 ×× 289 ×× (1 + 1.414) cm2
= 1395.415 cm2

Question: Calculate the area of octagon that has side 10 m.

Solution:

Given: Octagon side a = 10 m

The Area of octagon formula is given by,

Area of octagon = 2 a(1 + 2–√2)

Area of octagon = 2 (10 m)2 (1 + 2–√2)
Area of octagon =  2 ×× 100 m2 ×× 2.414

Area of octagon = 482.84 m2

The Area of octagon is 482.84 m2

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

Question: A octagon has side of 6 cm. Calculate the area of octagon.

Solution:

Given: Octagon side a = 6 cm

The Area of octagon formula is given by,

Area of octagon = 2 a2 (1 + 2–√2)

Area of octagon = 2 (6 cm)2 (1 + 2–√2)
Area of octagon = 2 ×× 36 cm2 ×× 2.414

Area of octagon = 173.82 cm2

The Area of octagon is 173.82 cm2.

How To Find Area Of Right Angled Triangle: Formula with Examples

How to Calculate Regular Octagon?

Candidates can calculate the area of a regular octagon with the standard regular polygon method, check above given examples to clear the concept of Area of an Octagon and practice more by using the given formulae.

We hope the above provided stuff in concern of Area of an Octagon will be beneficial for your, candidates having any query must comment in the below tuned comment box, our experts of recruitmentresult.com will surely solve it as soon as possible.

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