## Octagon Formula

An octagon is said to be regular if the lengths of all of its sides and the measurements of all of its angles are the same.

A polygon is a closed shape in two dimensions that is formed by connecting a series of straight-line segments. An octagon is a kind of polygon that has eight sides, as defined by geometry. An octagon is said to be regular if the lengths of all of its sides and the measurements of all of its angles are the same. To phrase it another way, the sides of a regular octagon are parallel to one another.

In a normal octagon, the internal angle and the outside angle both measure 135 degrees, while the angle between the two measures 45 degrees. The term “octagon formula” refers to a predetermined set of formulae that may be used to determine the area and perimeter of a regular octagon. These formulas have been specified in advance.

## Octagon Area Formula

The space that may be enclosed by an octagon’s eight sides is referred to as its area. Octagons are two-dimensional shapes having eight sides each. We may use the area of an isosceles triangle as a basis for our calculation of the area of the octagon.

After doing the necessary calculations, the area of the form is cut up into eight equal isosceles triangles and then reassembled. In a regular octagon, the length of each side is the same, and the angles formed by the intersection of adjacent sides are also the same. The measure of each inside angle is 135 degrees, whereas the measure of each external angle is 45 degrees.

The formula is:

2a^{2}(1+√2)

## Octagon Perimeter Formula

Octagon’s perimeter is equal to the length of the octagon’s border. Therefore, the perimeter will be equal to the total length of all of the sides. The calculation for the length of the perimeter of an octagon is done through the formula 8a.

a being the length of a side of the octagon

## Solved Examples

**Example 1: Find the area and circumference of an octagon with regular sides and a side length of 2.3 centimetres.**

**Solution:**

Provided in the question is:

Side length of the octagon is = a = 2.3cm

Area is:

2a^{2}(1+√2)

= 2(2.3)^{2}(1+√2)

= 25.54 cm^{2}