Count all the rectangles in the figure below, squares included.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
The figure is a rectangle cut into smaller rectangles by lines that do not all run across the whole figure. A rectangle is counted when all four of its sides lie on lines of the figure; a square is a rectangle too. Naming the corners and crossing points and counting by the number of small parts each rectangle covers makes sure none is missed or counted twice.
One part (5): ABFD, BCHF, DEJI, EGKJ, GHLK
Two parts (3): ACHD, DGKI, EHLJ
Three parts (1): DHLI
Five parts (1): ACLI
Total \(=5+3+1+1=10\) rectangles.
Why the other options are incorrect
Option (1) 9 — Incorrect. This leaves out the rectangle DHLI, which is made of three parts.
Option (2) 7 — Incorrect. This leaves out the 3 rectangles made of two parts, such as ACHD.
Option (4) 8 — Incorrect. This leaves out both the rectangles made of five parts and those made of three parts.