c. Are the areas of the two sheets of paper ever the same after each being folded \( n \) times? Explain how you know.

When you fold a sheet of paper in half, the area remains constant; it’s still the same piece of paper, just rearranged. However, the dimensions change, affecting how it fits into space. So, if you fold two sheets of paper the same number of times \( n \), their total areas will always be the same as the original sheets, regardless of the number of folds, since neither the material nor the quantity is altered. The fun twist is that with each fold, there’s a pattern to note: each folding in half reduces one dimension while keeping the area intact. So, if one was attempting to stack or fit the folded sheets together, the way they navigate space after folding might lead to some interesting geometric puzzles! You'd be amazed at how many shapes and sizes you can create through the art of folding alone!