I have a question from a school problem-solving homework sheet.
Here is the diagram of the problem:
Question: Two squares, A and B of the side lengths 6 cm and 5 cm respectively, overlap each other partially. Find the difference of the two shaded areas.

The difference of the two shaded areas is just the area difference of the two squares, i.e. $36 - 25 = 11\space \text{cm}^2$. The overlapping area simply cancels out in the difference.
An obvious case is where the smaller square is right inside the larger one.