Making a dome with four-sided panels with the same area

Hello. I'm doing a little architectural project and I can't get to solve one problem. I'm trying it also in the maths way, but I haven't get a solution yet. I hope you could help me. 

I want to do a dome with four-sided panels with the same area. The upper panel is free-form and I don't mind it's size. ¿How do you think I should work?

Thank you very much.