Count the number of squares in the figure below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
The figure is a square with both middle lines and a square joining the mid-points of its sides. A square is counted when all four of its sides lie on lines of the figure, whichever way it is turned. Naming the corners and crossing points and counting by the number of small parts each square covers makes sure none is missed or counted twice.
Two parts (4): ABED, BCFE, DEHG, EFIH
Four parts (1): BFHD
Eight parts (1): ACIG
Total \(=4+1+1=6\) squares.
Why the other options are incorrect
Option (1) 5 — Incorrect. This leaves out the square BFHD, which is made of four parts.
Option (2) 7 — Incorrect. This counts one square twice; the groups above add up to 6.
Option (4) 4 — Incorrect. This counts only the 4 squares made of two parts, the smallest ones.