Join the two brocades together to make one large square cushion-cover. 

How can you do this so as to mutilate the material as little as possible? 
Make the cuts only along the lines that divide the little chequers.

I cut the two squares in the manner desired into four pieces that would fit together and form another larger square, taking care that the pattern should match properly, and when I had finished I noticed that two of the pieces were of exactly the same area; that is, each of the two contained the same number of chequers. 

Can you show how the cuts were made in accordance with these conditions?

See answer