Proportional UV unwrapp issue

Hi everybody.
I’m new in Blender, trying to do a relatively simple thing.


I have a jigsaw chip model. And I have a thin plane layer on top of the model - that will be a place for texture. And of course, texture should be proportional to model and have no distortions or stretches - it will be generated and applied in runtime.
So my question is, why do I have that distortion on the left when I unwrap? No matter which method is used - angled or conformal.

Have you tried dividing the large ngon into tris/quads

Please attach or supply a link to your blend file

A friend of mine made this couple of models really quickly.
Basically for each one of them I need a 1:1 unwrap without any distortions.

https://dl.dropboxusercontent.com/u/100484639/puzzle.blend

Thanks!

A friend of mine made this couple of models really quickly.
Quickly = lazy = poor unwrap

Adding some cuts will overcome the problem


Tell your friend to do a better job next time

Could you please give me steps on how to fix it for all my models? These are basically test models, so no point in telling him=)