I think you're missing the point. Its not that these are complete proofs or easy to understand proofs. The idea of a proof without words is that by staring at

I think you're missing the point. Its not that these are complete proofs or easy to understand proofs. The idea of a proof without words is that by staring at it and thinking about it, you can work out why the statement/theorem is true. That being said, you're right that you need to be careful, as pointed out by Russel O'Conner's proof that 32.5 = 31.5 (with the colored triangles). However, someone who uses that as a "proof" is doing it wrong. When you find a proof without words, you need to actually write out the formulas that the picture indicates and make sure everything adds up (at least, for proofs of type you mentioned such as proving that areas are equal).