Count all the rectangles in the figure below, squares included.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30
The figure is a grid of 4 × 2 small rectangles. Every rectangle in it is fixed by choosing 2 of the 5 vertical lines and 2 of the 3 horizontal lines; a square is a rectangle too.
Ways to choose 2 vertical lines: \(\displaystyle\frac{5\times4}{2}=10\)
Ways to choose 2 horizontal lines: \(\displaystyle\frac{3\times2}{2}=3\)
Rectangles \(=10\times3=30\)
Why the other options are incorrect
Option (2) 11 — Incorrect. This counts only the 11 squares.
Option (3) 41 — Incorrect. This counts the 11 squares twice, once as squares and once again as rectangles.
Option (4) 19 — Incorrect. This leaves out the 11 squares, which are rectangles too.