Getting the chord length of a regular hexagon
chord = radius - tan(30) * offset * 2
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Woah, hold up, you’re still here? I’m flattered, this is way longer than I would have spent at any site with math explanations.
Getting this formula requires a little bit of work with triangles and trapezoids. Let’s mirror the hexagon across the X axis so everything is upright, and then work with the left portion of chord.
Yeah, kind of like that.
Working with regular hexagons gives us a couple of things for free. Let’s break it down.
Regular hexagons all have 120 degree angles, so by cutting the hexagon in half, we know we’re working with a 60 degree angle. If you haven’t noticed or scrolled far enough down yet, you’ll notice there’s a triangle adjacent to our trapezoid.
The length of the chord/2 is the radius - line segment F — H. This is easy to compute, it’s a right triangle. Bring yourself back to high school trig, and the rest is easy.
In case you’ve forgotten, we use TOA, tan(θ) = adj/opp
So that is: tan(30) = offset/segment F — H
Subtract this value from the radius, then multiply it by two, and congrats, you have the chord length.
Q: But Darrien, couldn’t I solve this in 30 minutes?
A: Yeah of course you could, I did, but a Google search is way quicker.
Q: Will this work if I rotate my hexagon 90 degrees?
A: No. You’ll have to use the minimal radius if you want that to work. Throw your radius into this formula, cos(30) * radius and then throw a party.
Q: What about 180 degrees
A: Detention
Have a good day readers.
