The sides of an octagon

Subject: Octagon problem

How do I figure the length of the sides of an octagon when all I know is the diameter (4.375).

Craig

Middle
Parent

Thank you,

Hi Craig,

For the regular octagon in the diagram below let a be the length of each side. From the symmetry, the triangle PQR is a right triangle with two sides of equal length. I have called this length b.

From the theorem of Pythagoras, b² + b² = a² and hence

Again looking at the diagram 4.375 = b + a + b =

Now you can solve for a.

Cheers,
Penny Go to Math Central