The understanding here is that πr^2 is the area of a circle. You are saying that this understanding is important/useful even without the proof. This is in dir

The understanding here is that πr^2 is the area of a circle. You are saying that this understanding is important/useful even without the proof. This is in direct contradiction to what you said earlier, where you said the proof was important/useful even without the understanding. Perhaps we're using the word "understanding" to mean two different things here and that's where the contradiction lies.