[Unknown Target]

Hey guys, I need this done and I can't for the life of me find the right equation for it/have the time to figure out how to do it. What is the radius of an octagon (8-sided polygon) that is 28 feet across, with 12 and a half foot sides? (If that's possible...otherwise just the 28 foot across one please). Also, if no one would mind, what's the radius of another octagon that is 27 feet, two inches across? Thanks

[Bobboau]

ummmmm..... if it's 28 feet across then shouldn't it have a 14 ft radius?

12.5 ft sides on an octigon... lets see here, you would have an isosceles triangle with the two sides of length R and one os size 12.5 the central angle would be 45 degrees (the others would be 67.5)

hmmmm... 16.3........ish

[pecenipicek]

umm, thats basic math.


which i'm not in the mood to divulge too much, but considering logic of only 28 foot across

d=diameter
r=radius
d=28
r=28/2
r=14

however, that is only going to be true for the points, aka the every point of the octogon is going to be at that distance from the center.

however, i dont think that with 12 and half foot sides its diameter equals 28 feet.
lesee. pitagoras theorem says that
c^2=a^2+b^2
lets assume that a and b are 14
14^2+14^2=c^2

c^2=392
c=root of 392
c=19.79898987 (my calculator rounds it off like that)

and i just realised that pitagora's theorem doesnt apply in this case.
okay. take two. trigonometry this time.

lemme remind myself how it goes, however i think that a 28 feet octogon cant have 12.5 feet sides. gonna have to convert to centimeters.

[pecenipicek]

lesee, a 28 feet diameter octogon with 12.5 feet sides is not possible, simple trigonometry says so. i'll post the stuff later, i'm not in the mood to retype.

verify it yourself if you want.

i'm gonna calc you the length of the side with the radius being 14 feet and the other wee bit smaller value.

edit, okay, via trigonometry again, i found the side.

its length is 10.52673247 feet.

thank you very much.

i'm so bored i'm solving trigonometry



the other ones radius is 13.58333333 feet.

[pecenipicek]

anyone care to verify my calcs?

[Descenterace]

Can someone please define 'radius' as it applies to polygons? Is it the radius of the largest circle that fits wholly within the polygon, or the radius of the smallest circle that wholly contains the polygon?

[Flipside]

It's the radius of a circle which fits exactly outside the polygon iirc.

[pecenipicek]

i just realised my calcs are wee bit off.

by some 2-5 feet or more.

[Unknown Target]

So then what's the answer?

[Descenterace]

Also, does '28 feet across' mean maximum or minimum, ie. corner to corner or mid-side to mid-side?

If it's corner to corner, then the radius is simply half the diameter. Which is as it should be.

[CP5670]

You can't have a regular octagon with those conditions. If it has 12.5 sides, it will be a little over 30 wide. If you take only the 28 wide condition, the octagon's sides will be 11.6 each and the radius is either 14 or 15.154, depending on how you're defining that for a polygon.

[Unknown Target]

Thanks guys, works now