I'm building a three legged sculpture stand. I would like to construct a hexagon in which:
- Every other side is of equal specific lengths (Lengths of sides: a b a b a b).
- Opposing sides are parallel.
I hope the above summarises in words what I want to do. It should look approximately like this:
But the short respectivly long sides should be of specific lenghts, in my case the short sides should be 45 and the long sides 280. How can I construct that?
I am drawing in a cad-program and have constructed this in the way below, but I'm also interested in construction on paper.
My research so far
The angle sum of a hexagon is 720°, so each side is 120°. In the cad-program I can easily draw the figure by starting with a line of length 45, then draw a connected line of length 280 at angle 120° to the first line and so on. But on paper, using a goniometer, this wouldn't be very exact.
One approach: Start with an equilateral triangle of side length $45+280+45$ and chop off 3 equilateral triangles of side length 45 from the vertices.