Take a right angled triangle whose two shorter sides are 6cm long and 8cm long. Draw squares on each of those sides. Add their areas—36 and 64 sq cm, respectively. What you get is, as Pythagoras told us a long time ago, the area of the square on the longest side, 100 sq cm.
Martin Gardner would have been 100 this week. I think it’s just possible that had he been alive, he might have celebrated the day with Pythagoras, showing with actual cut-out cardboard squares how the two smaller squares add up to the large one that marked his age. After all, in a celebrated 1998 essay in the New York Review of Books, Gardner debunked what was called the “new new math": new ideas for teaching the ancient subject. In particular, he remarked on how it “taught" Pythagoras’ famous theorem, producing college students who hadn’t grasped that, fundamentally, it is “about geometric squares."
Whereas, if you simply use squares, you put the idea in their heads straight away, never to escape.