**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 135^{o}. 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 ×× a^{2} ×× (1 + 2–√2)

= 2 ×× 9^{2} ×× (1 + 2–√2) cm^{2}

= 2 ×× 81 ×× (1 + 1.414) cm^{2}

= 391.103 cm^{2}

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 ×× a^{2} ×× (1 + 2–√2)

= 2 ×× 17^{2} ×× (1 + 2–√2) cm^{2}

= 2 ×× 289 ×× (1 + 1.414) cm^{2}

= 1395.415 cm^{2}

**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^{2 }(1 + 2–√2)

Area of octagon = 2 (10 m)^{2} (1 + 2–√2)

Area of octagon = 2 ×× 100 m^{2} ×× 2.414

Area of octagon = 482.84 m^{2 }

The Area of octagon is** 482.84 m ^{2}**

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 a^{2} (1 + 2–√2)

Area of octagon = 2 (6 cm)^{2} (1 + 2–√2)

Area of octagon = 2 ×× 36 cm^{2} ×× 2.414

Area of octagon = 173.82 cm^{2}

The Area of octagon is** 173.82 cm ^{2}.**

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.

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