Make Hexagon the same area as Rectangle's area

Hi all,
I guess it could be a very basic math issue…but I cannot figure it out…
I have a rectangle, I know its area.
And I want to use the rectangle’s area to constraint the hexagon’s area. I mean, make them the same.
But and the sametime I want to be able to control the shape of the hexagon on Y axis.
I thought I can use the Scale NU to achieve it but I have to do it manually to try many times on both X & Y scale factor. I wonder if there is any way that I just need to define the “Y scale factor”, then it can automatically work out the number of “X scale factor”.
I know you can do it via Galapagos but I don’t like it, because you need to wait for it. It must be some mathematics or geometric ways to achieve what I want…

Thanks for any suggestion
Rec & Hex.3dm (13.6 MB)
Rec & (14.1 KB)

Given the halfAngle the Area (A), Radius(R) equation of a regular polygon: (11.4 KB)

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Check out Pufferfish plugin scale to area component. Can scale any shape to desired area with X and Y factor controls.

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Got it, thanks Pfotiad0, thanks Michael.

Given the opportunity a good challenge (via K2 or the Recursive way) is to find an inscribed (to R) polygon with N sides (that are not equal) that yields the same Area (A) to the regular one. Obvioulsy there’s many solutions possible for that.

Yes, I have try a mathematics way to achieve it, though the definition doesn’t look that neat…Hex.3dm (42.8 KB) (22.1 KB)

Thanks Kim, but with this formula I think it cannot deform the hexagon when maintaining the same area as below?

As @Michael_Pryor mentioned above, you could use Scale To Areain Pufferfish plugin.

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In fact by “non equal sides” I mean that type of stuff (this C# is using Recursion instead of K2):

Thanks HS and Peter