Polygon by area with the same fillet radius

I have to do a circle, a triangle a square and a pentagon with the same area. I took the area of the circle and succeed to give them the same area. The problem is that I need them to have the same fillet radius with an especific value (30mm), but with the number or number slider imput it makes it proportional and not by units, so the radius is not the same for the three polygons corners.

The only way I was able to round the vertices was by adding an imput at the end of the formula, but it changes the area. My attemts of adding the fillet imput after the polygon comand and before the area one were disastrous

Any Idea?

You’ll either have to do it analytically, figuring out the area of a triangle plus fillets, or you have to solve it iteratively. You can do the latter using Galapagos, the former using maths.

area target.gh (16.5 KB)

area%20finder