How many rectangles are there in the figure given below? (A square is also a rectangle.)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 15
The figure is a grid of 5 × 1 small rectangles. Every rectangle in it is fixed by choosing 2 of the 6 vertical lines and both horizontal lines (the top and the bottom); a square is a rectangle too.
Ways to choose 2 vertical lines: \(\displaystyle\frac{6\times5}{2}=15\)
There are only 2 horizontal lines, the top and the bottom: 1 way
Rectangles \(=15\times1=15\)
Why the other options are incorrect
Option (1) 10 — Incorrect. This leaves out the 5 squares, which are rectangles too.
Option (2) 20 — Incorrect. This counts the 5 squares twice, once as squares and once again as rectangles.
Option (3) 5 — Incorrect. This counts only the 5 smallest rectangles.