# Area of an octagon

How to calculate the area of an octagon. With worked examples.

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## How to calculate the area of an octagon

There area two main methods to calculate the area of an octagon.

### Method 1:

If you know the length of “H” as well as “B” the length of one of the 8 sides, then you can use this method.

The octagon is made up of 8 triangles, so find the area of one triangle and multiply by 8.

## Example

The total heightA of the octagon is 16.9m and the length of a side “B” is 7m, calculate the area.

A = 16.9m

B = 7m

First calculate the area of one triangle

Area of a triangle = 0.5 x Base x Height

The height of one triangle = A ÷ 2  = 16.9 ÷ 2 = 8.45

Area of a triangle = 0.5 x Base x Height

Area of a triangle = 0.5 x 7m x 8.45 = 29.575m2

There are 8 triangles in an octagon, so 29.575m2 x 8 = 236.6m2

Answer = 236.6m2

## Method 2:

You can use method two if you only know the length of one of the 8 sides.

## Example

The length of one of the 8 sides “B” is 7m, calculate the area of the octagon.

B = 7m
The area of an octagon = 2 x (1 + √2) x B2
Area = 2 x (1 + 1.414213562) x 72
Area = 2 x (1 + 1.414213562) x 49
Area = 2 x (2.414213562) x 49
Area = 4.828427124 x 49
The area of an octagon = 236.6m2

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