24898

First we worked out the total area by working out the individual areas of the squares and adding them together. The answer was 1056.

Then we divided 1056 by some two digit numbers. The only one that gave us a sensible interger for an answer was 1056 divided by 16 which equaled 66.

But we had another problem - the biggest square was 18x18 and wouldn't fit in. So we doubled 16 and halved 66 which gave us 32x33. Now all we had to do was fit the pieces together to make the rectangle.

18 and 14 made a 32 side and 18 and 15 made a 33 side all we had to do is get the other sides done and fill in any gaps.

Here is our result: