|The Squared Square|
Because there is much other online information on this topic, I have elected to share only a couple of examples.
"Squaring the square" with areas of different sizes was long considered
to be impossible. In 1939, however, R.P. Sprague of Germany published a
55-square solution. A major "improvement" upon that discovery was
this 26-square layout, first published by W.P. Tutte of Canada in 1940:
Subsequently, it has been shown that the lowest-order possible solution is 21 squares. The matrix shown below, believed to be unique, was discovered in 1978 by W.A. Duijvestijn of The Netherlands: