I'm a beginnner with Blender and I try to train myself watching videos tuts, but today I'm confronted with a small problem that I can't find the answer.

As the pictures describe better than the words, I made a small picture describing my problem.

My problem is that I can't get a UV Map with the right size and the correct deformation. I tried several things but I can't do it. Could you please help me to fix my problem and especially to understand how to do it.

enter image description here