Conclude by giving your students these challenges:
The two rectangles below are congruent, and the area of each is 10. What's the area of the shaded figure?
Here's the solution: Start by labelling the sides, and cutting the quadrilateral along one of its diagonals, as illustrated:
The diagonal has cut our shaded quadrilateral into two triangles. Each triangle has a base of \(x,\) and a height of \(y.\) So the area of each triangles is \(xy/2.\) We have two such triangles, so the shaded area must be \(xy.\) But \(xy\) is also the area of each rectangle, which is \(10.\) Thus, the area of the shaded figure is \(10.\)