Adjusting polygon segments lengths whlie keeping area constant

Hello,

I have an estimated polygon of a site area according to some rules and datas that i have. I want to change each length of this polygons segments, while keeping its area contstant as possible. The point is trying to find the polygon with intended area and lengths proximate to first one(so do i need to add some pull forces to vertices? another question) I'm adding gh file below.

Thanks