Area Calculator

To find the octagon area, all you need to do is know the side length and the formula below:

The octagon area may also be calculated from:

Octagon Area = perimeter × apothem / 2

A perimeter in octagon case is simply 8 × a. And what is an apothem? An apothem is a distance from the center of the polygon to the mid-point of a side. At the same time, it's the height of a triangle made by taking a line from the vertices of the octagon to its center. That triangle - one of eight congruent ones - is an isosceles triangle, so its height may be calculated using, e.g., Pythagoras' theorem, from the formula:

h = (1 + √2) × a / 4

So finally, we obtain the first equation:

Octagon Area = perimeter * apothem / 2 = (8 × a × (1 + √2) × a / 4) / 2 = 2 × (1 + √2) × a²