# Area Of An Octagon Formula

## Area Of An Octagon Formula

Polygons are two-dimensional closed figures made up of three or more line segments. Triangles are the smallest polygons having three sides. Similarly, a polygon with eight sides is known as an octagon. A regular octagon is one with eight sides that are all the same length and have equal angles between them. In a normal octagon, each inner angle measures 135 degrees. The outer angles are 45 degrees each.

This lesson teaches you how to calculate the area of an octagon. Also, how to construct a formula for the same and solve various instances to ensure that you grasp the concept.

## What is an Octagon Formula?

A polygon is a two-dimensional (2-D) closed shape composed of straight line segments. In geometry, an octagon is a polygon with eight sides. A regular octagon is one with equal lengths on all sides and angles. In other words, the sides of a standard octagon are congruent. In a normal octagon, the internal angle is 135°, while the external angle is 45°. There is a standardised set of formulae for calculating the perimeter and area of a regular octagon, known as the octagon formula.

## Formula for an Area of an Octagon

The formula used to calculate the area of an octagon is:

Area of an Octagon = 2s2(1+√2)

where s is the length of the side of the octagon.

## How to Calculate Area of Octagon?

The calculation of the area of the octagon can be done using the Area Of An Octagon Formula.

Octagons have an area of 2s2(1+√2). The octagon’s area may be calculated using the procedures outlined below.

Step 1: Determine the length of the side of the octagon.
Step 2: Calculate the square of the length of the side.
Step 3: Calculate the product of the square of its length and 2(1+√2). This will tell you the area of the octagon.
Step 4: To calculate the area of an octagon, use the formula 2s2(1+√2) and substitute the appropriate numbers.
Step 5: Express the answer in square units.

## Properties of Regular Octagon

Before we proceed to calculate the area of an octagon formula, let us first review some of the important properties of a regular octagon.

• It has eight sides and eight inner angles.
• All sides are the same length, and all angles are the same dimension.
• A regular octagon contains 20 diagonals.
• Each inner angle is 135 degrees. Thus, the total of all internal angles is (135 x 8) = 1080 degrees.
• Each external angle is 45 degrees. Thus, the total of all outside angles is (45 x 8) = 360 degrees.

### Solved examples Using Octagon Formula:

Example 1: Calculate the area of the octagon if the length of the side of the octagon is 16 in.

Solution:

Length of the side, s = 16 in

Using the formula for the area of the octagon,

A = 2s2(1+√2)

A = 2 ×162(1+√2)

A = 1236.08 square inches

Therefore, the area of the octagon is 1236.08 square inches