Count all the rectangles in the figure below, squares included.

The correct answer is Option (4) → 36

The figure is a grid of 3 × 3 small rectangles. Every rectangle in it is fixed by choosing 2 of the 4 vertical lines and 2 of the 4 horizontal lines; a square is a rectangle too.

• Ways to choose 2 vertical lines: \(\displaystyle\frac{4\times3}{2}=6\)

• Ways to choose 2 horizontal lines: \(\displaystyle\frac{4\times3}{2}=6\)

• Rectangles \(=6\times6=36\)

Why the other options are incorrect

• Option (1) 18 — Incorrect. This counts only the rectangles that are one row high.

• Option (2) 14 — Incorrect. This counts only the 14 squares.

• Option (3) 50 — Incorrect. This counts the 14 squares twice, once as squares and once again as rectangles.