How many parallelograms are there in the following figure?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 30
Every parallelogram in the figure is bounded by two of the slanting lines and two of the horizontal lines. So the count is the number of ways of choosing 2 slanting lines times the number of ways of choosing 2 horizontal lines.
Slanting lines 1 to 5, each running the full height: pairs \(\displaystyle =\frac{5\times4}{2}=10\)
Horizontal lines a, b, c, each running the full width: pairs \(\displaystyle =\frac{3\times2}{2}=3\)
Parallelograms \(=10\times3=30\)