Practice!

Sample Problem

How many rectangles are in the picture?

  rectangles

Solution

We could count individual rectangles to get 9 + 12 + 6 + 4 + 4 + 1 = 36, but since the rectangles here are laid out in a regular grid, we can take the shortcut. There are 4 × 3 ÷ 2 = 6 segments in the width and 4 × 3 ÷ 2 = 6 segments in the length of the larger rectangle. Thus the total number of rectangles in the picture is 6 × 6 = 36.