# Octagon Formula

A polygon having eight sides is known as an octagon. If all the sides of an octagon are equal and angles are the same then the octagon is called a regular octagon. A regular octagon has a total number of 20 diagonals. The sum of all interior angles of a regular octagon is 1080 degrees. Also, each interior angle is 135 degrees. The exterior angle of an octagon measures 45 degrees and the sum of all exterior angles is 360 degrees. The octagon formula is used to calculate its area, perimeter of an octagon. Learn about the octagon formula with few examples given below.

## What Is Octagon Formula?

The octagon formula is used to calculate the area, perimeter, and diagonals of an octagon. To find the area, perimeter, and diagonals of an octagon we use the following octagon formulas.

### Formulas for Octagon:

To find the area of an octagon we use the following formula: Area of octagon formula = 2 × s^{2} × (1 + √2)

To find the perimeter of an octagon we use the following formula: Perimeter of octagon = 8s

To find the number of diagonals of an octagon we use the following formula: Number of Diagonals = n(n - 3)/2 = 8(8 - 3)/2 = 20

where,

- s = side length
- n = number of sides

## Examples Using Octagon Formula

**Example 1:** Calculate the perimeter and area of an octagon having a side equal to 4 units using the octagon formula.

**Solution:**

To Find: Perimeter and Area

Given: s= 4 units.

Using the octagon formula for perimeter

Perimeter(P) = 8s

P = 8 × 4

P = 32 units

Using the octagon formula for area

Area of octagon = 2s^{2}(1 + √2)

= 2 × 4^{2}(1 + √2)

= 77.25483 units^{2}

**Answer:** Perimeter and area of the octagon are 32 units and 77.25483 units^{2}.

**Example 2:** An octagonal board has a perimeter equal to 24 cm. Find its area using the octagon formula.

**Solution:**

To Find:** ** Area of the octagon.

Given: Perimeter = 24 cm.

The perimeter of octagon = 8s

24 = 8 s

s = 3 cm.

Using the octagon formula for area,

Area of octagon = 2s^{2}(1 + √2)

= 2 × 3^{2}(1 + √2)

= 43.45 cm^{2}

**Answer: **Area of octagonal board is 43.45 cm^{2}.