How many rectangles are there in the figure given below? (A square is also a rectangle.)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 10
The figure is a grid of 4 × 1 small rectangles. Every rectangle in it is fixed by choosing 2 of the 5 vertical lines and both horizontal lines (the top and the bottom); a square is a rectangle too.
Ways to choose 2 vertical lines: \(\displaystyle\frac{5\times4}{2}=10\)
There are only 2 horizontal lines, the top and the bottom: 1 way
Rectangles \(=10\times1=10\)
Why the other options are incorrect
Option (2) 6 — Incorrect. This leaves out the 4 squares, which are rectangles too.
Option (3) 14 — Incorrect. This counts the 4 squares twice, once as squares and once again as rectangles.
Option (4) 4 — Incorrect. This counts only the 4 squares.