Area of an octagon

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 height “A” of the octagon is 16.9m and the length of a side “B” is 7m, calculate the area. A = 16.9mB = 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 = 8.45Area of a triangle = 0.5 x Base x HeightArea of a triangle = 0.5 x 7m x 8.45 = 29.575m²There are 8 triangles in an octagon, so 29.575m² x 8 = 236.6m²Answer = 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 = 7mThe area of an octagon = 2 x (1 + √2) x B²Area = 2 x (1 + 1.414213562) x 7²Area = 2 x (1 + 1.414213562) x 49Area = 2 x (2.414213562) x 49Area = 4.828427124 x 49The area of an octagon = 236.6m²