I saw the following problem on the Internet a few years ago.
Let T be a triangle with side lengths a, b, and c. Let T' be a triangle with side lengths a', b', and c'. Suppose a < a', b < b', and c < c'. Must it follow that Area(T) < Area(T')?
The answer is quite simple, but surprising to most people. It makes a good question to put to a beginning geometry class.
If you need to, you can find the answer here.