How many rectangles are there in the figure?

The correct answer is Option (4) → 100

The figure is a 4 by 4 grid, drawn with 5 horizontal and 5 vertical lines. Every rectangle (squares included) is fixed by choosing two horizontal lines for its top and bottom and two vertical lines for its sides, and every such choice gives a different rectangle.

• Ways to choose 2 of the 5 horizontal lines: \(\displaystyle \frac{5\times4}{2}=10\)

• Ways to choose 2 of the 5 vertical lines: 10

• Rectangles: \(10\times10=100\)