How to generate a quad using a given area


I’m exploring some generative design techniques. Currently, I’m trying to find a way to draw a random quad shape using just a given area to go by. I have tried to achieve this using a cuboid (as in the screenshot below), but obviously this would yield only right-angled shapes.

Also, I’m not sure how to go about having only the area as an input. I guess I could maybe plug in a randomizer to one of the variables?

Any pointers would be appreciated.

You could start with a square, give it a random rotation and shear two sides:

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That’s an interesting approach. Although it only generates parallelograms. I was thinking of going even further and generating anything with four sides.
On a side note, I noticed the polygon approaches a rectangle the larger the area input is. I solved it by changing the scale factor to this:

Going back to the initial problem, I found this formula here which relates the area of any quad.

I’m still trying to think of a good way to incorporate it.