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.

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

With Radius

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

Let us solve an example to understand the concept better.

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