Octagon math

[Dave Zellers]

Had a friend ask me if there was a formula for calculating the length of a side of a 4" octagon- (4" side to side, not point to point).

Told him I didn't know but I would draw it in my CAD program and that would get him close enough. So I sent him this drawing but now I'M wondering if there is a way to calculate it. I used to be pretty good with geometry but that is now a fer piece back.

Anybody know? (I fear it's going to be simple and I'll have a DOH! moment) :)

444164

[Mike Henderson]

Take the diameter of the circle that the octagon is inscribed in and multiply it by 0.383. That's the length of each side. If you start with the length of a side just work the equation backwards to find the diameter.

The more interesting one is the hexagon because each side is equal to the radius.

Mike

[John K Jordan]

Like most math questions these days there's an on-line calculator for that. For example: https://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
Set to calculate everything for a given inradius, units=inches, set inradius=2, sides=8, pick the number of significant figures. Click Calculate.

The math isn't all that hard but the calculator is quick (and fun to play with)

JKJ

[Dave Zellers]

Like most math questions these days there's an on-line calculator for that.
JKJ
Yes- Thanks! I couldn't get it out of my head and I found this one-

https://www.omnicalculator.com/math/octagon

Great stuff.

[Dave Zellers]

Take the diameter of the circle that the octagon is inscribed in and multiply it by 0.383. That's the length of each side. If you start with the length of a side just work the equation backwards to find the diameter.

DANG man, talk about nailing the answer to the question! Very cool. The second part about hexagons is absolutely cooler.

I love geometry. Thanks!

[Bill Dufour]

https://www.mathopenref.com/polygonsides.html

[Dave Zellers]

https://www.mathopenref.com/polygonsides.html

Very cool site- thanks! Wow- the stuff that is out there...

[Bill Dufour]

For Algerba students and parents I recommend.

https://www.purplemath.com/

[Steve Demuth]

Well, it's pretty simple. If it's 4" across, it's 2" center to side. There are 8 sides, so the included angle of a wedge that includes one side is 360o / 8 = 45o. So, half of a wedge is right triangle with one side 2" and adjacent angle of 22.5o (half the included angle). The side's length is thus 2 * 2" * sin(22.5).

[Mark Hennebury]

x 0.4142 Gets you pretty close. ( that's the 4" side to side measurement x 0.4142)