An octagon is a shape with eight sides and eight angles. It is a polygon, which means it is a closed figure with straight sides. Each angle in an octagon measures 135 degrees. The sum of all the angles in an octagon is 1080 degrees. The word “octagon” comes from the Greek words “okto,” meaning eight, and “gonia,” meaning angle.

## Area of an Octagon Formula

The area of an octagon is the measure of the region enclosed by the octagon. It is the amount of space inside the octagon. It is usually measured in square units, such as square inches, square centimeters, or square meters.

The area of an octagon can be calculated using different formulas, depending on whether the octagon is regular (all sides and angles are equal) or irregular (sides and/or angles are different).

For a regular octagon, the formula to calculate the area is:

**Area of a regular octagon A = 2(1 + √2) × s ^{2}**

where A is the area of the octagon, s is the length of one of its sides, and √2 is the square root of 2 (approximately 1.414).

## Area of an Octagon Formula

An irregular octagon is a type of octagon that does not have all of its sides and angles equal. In other words, an irregular octagon is a polygon with eight sides where the sides are of different lengths and the angles between the sides are not all the same.

To calculate the area of an irregular octagon, you can use the following formula:

A = 2 × (1 + √2) × s_{1} × s_{2}

where A is the area of the octagon, s_{1} is the distance between two opposite sides of the octagon, and s_{2} is the distance between two adjacent sides of the octagon.

### Area of an Octagon Examples

Sure, here are some examples of how to calculate the area of an octagon using the formula:

**Example 1:Let’s say we have a regular octagon with a side length of 6 cm.**

To find the area, we can use the formula:

A = 2 × (1 + √2) × s^{2}

Area of an Octagon= 2 × (1 + √2) × 6^{2}

A = 2 × (1 + √2) × 36

A ≈ 309.96 cm^{2}

Therefore, the area of this octagon is approximately 309.96 square centimeters.

**Example 2: Let’s say we have an irregular octagon with two sides of length 8 cm, two sides of length 6 cm, and four sides of length 5 cm. To find the area, we need to break down the octagon into smaller shapes. **

We can split the octagon into a rectangle and four triangles:

- The rectangle has a length of 6 cm and a width of 8 cm.
- The four triangles have a base of 5 cm and a height of (8 – 6) / 2 = 1 cm.

To find the area of the rectangle:

A = length x width

A = 6 x 8

A = 48 cm^{2}

To find the area of one triangle:

A = 1/2 x base x height

A = 1/2 x 5 x 1

A = 2.5 cm^{2}

Since there are four triangles, the total area of the triangles is 4 x 2.5 = 10 cm^{2}.

The total area of the octagon is the sum of the area of the rectangle and the area of the triangles:

A = 48 + 10

A = 58 cm^{2}

Therefore, the area of this irregular octagon is 58 square centimeters.