How many rectangles are there in the figure given below? (A square is also a rectangle.)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 9
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): ABHG, BCFD, DEKJ, EFLK, GHJI
Two parts (2): ABJI, DFLJ
Three parts (1): BCLJ
Five parts (1): ACLI
Total \(=5+2+1+1=9\) rectangles.
Why the other options are incorrect
Option (1) 7 — Incorrect. This leaves out both the rectangles made of five parts and those made of three parts.
Option (3) 5 — Incorrect. This counts only the 5 smallest rectangles, the ones that are a single part each.
Option (4) 8 — Incorrect. This leaves out the whole rectangle ACLI, which is made of five parts.