The task.
A sheet of paper ABDE is folded in such a way that one of its vertex (D) will lie on the side that is opposite to that vertex . Thus, there will be different folding lines depending on the position of vertex D on side AB. For example, vertex D becomes point G to form triangle GBH. If the length of side DB is 3 dm, explore what happens to the area of triangle GBH when point G is moved along side AB.

Comment: While representing the problem, some participants mentioned that it was important to also focus on the area behavior of triangle GHI.