Count the number of rectangles in the given figure.

Concept: To count every rectangle in a figure built from overlapping squares, do not stop at the obvious ones -- systematically combine adjacent basic regions and group the resulting rectangles by how many basic regions each one spans. A rectangle can be formed by merging any number of aligned regions, and every square is itself a rectangle, so squares must be counted too.

The figure may be labelled as shown.

Group the rectangles by how many basic regions each is composed of:

Adding across every group: 8 + 5 + 4 + 3 = 20 rectangles in total (squares are counted among rectangles, since a square satisfies every condition of a rectangle).

Cross-check: the figure has four-fold rotational symmetry about the centre O, so a genuine rectangle family should split evenly across the figure's four congruent wings when rotated by 90 degrees. The 2-region, 6-region and 8-region groups each divide cleanly this way (with ABCD standing alone as the single outer square), confirming that no combination has been missed or double-counted.