How long should each side be for an octagon 13 feet in diameter?

Answer 1

For a regular octagon, the angle for each side of an octagon is 180 x (8 - 2) / 8= 1080 / 8 = 135 degrees.

Observe that 135 = 90 + 45.

So, if we split up the octagon's angles on one side into 90 and 45 degree angles, we will get two 45-45 triangles, and a square.

The length of the sides for a 45-45 triangle is 1/1/√2, or, more generally, x/x/x√2.

The diameter of an octagon in relation to the sides is 2√2x+x = (1 + 2√2) * x.

Solve for x:

(1 + 2√2) * x = 13

Divide by (1 + 2√2), isolating x:

x = 13 / (1 + 2√2) = 3.39565...

The length of each side of an octagon with a diameter of 13 feet is approximately 3.39 feet, or 13 / (1 + 2√2) feet.