Here's the challenge:

It is easy to compare the areas of some shapes of pattern blocks. The red trapezoid, for example, is half the area of the yellow hexagon and three times as large as the green triangle. How do the areas of the orange square and tan parallelogram compare?

Here's the solution:

If you build two "houses," one using a square and a triangle and the other using two tan parallelograms and the same size triangle, both houses have the same area. (They are congruent.) Therefore, the area of the square is the same as the area of two tan parallelograms, which makes the square twice as large.