# Area of Octagon

The area of an octagon is the total amount of space that is enclosed by all its eight sides.

Since an octagon is a two-dimensional figure, the unit of its area is expressed in square units such as sq. cm, sq m, sq yd, sq ft.

## Formulas

### With Side Length

This is the basic formula to find the area of an octagon, which is given below:

Let us solve an example to understand the concept better.

Calculate the area of a regular octagon whose side length is 2.5 cm

Solution:

As we know,
Area (A) = 2s2(1 + √2), here s = 2.5 cm
= 2 × (2.5)2 (1 + √2)
= 30.177 sq. cm

### With Apothem and Perimeter

The formula to find the area of an octagon with apothem and perimeter is given below:

Let us solve an example to understand the concept better.

Finding the area of an octagon when the APOTHEM and PERIMETER are known

Find the area of a regular octagon whose perimeter is 128 cm and apothem is 12 cm.

Solution:

As we know,
Area (A) = 1/2 × P × a, here P = 128 cm, a = 12 cm
= 1/2 × P × a,
= 1/2 × 128 × 12
= 768 sq. cm

The formula to find the area of an octagon with radius is given below:

Let us solve an example to understand the concept better.

Finding the area of an octagon when the RADIUS is known

Find the area of a regular octagon whose radius is 12.5 cm.

Solution:

As we know,
Area (A) = 2√2r2, here r = 12.5 cm
= 2√2 × (12.5)2
= 441.94 sq. cm