Inspired by a mail from Robert Henderson (USA), en after some research by Aad van de Wetering (The Netherlands), we came with the following challenge.

Make a figure using four of the same pentominoes
Make a congruent figure using all the tetrominoes.
Try to minimize the areas of the surrounding rectangles..

Using four X-pentominoes this challenge is impossible to do. Aad van de Wetering showed his proof.
If you know any other proof, please mail it to us.

This will make the search easier

'Flat Poly2', a programm by Aad van de Wetering, can be of great assistance when trying to find a solution. 2.
 It can be downloaded at his site .