The diagram shows a shape made from six squares, each measuring one centimeter by one centimeter. The shape has a perimeter of length 14 centimeters. The zigzag shape is continued until it has 2,013 squares. What is the length of the perimeter of the new shape? We note that no matter how far the shape is continued and how many squares it contains, the first square and the last square will share one side with a neighbor and so have three edges exposed. Whereas the middle squares will share two sides with a neighbor and only have two edges exposed. So we can tally up the exposed sides and obtain our perimeter. We have a total of three exposed sides from the first square, 2,011 middle squares with two sides exposed each and then the last square contributes three sides. This gives us a total of six plus 4,022 or 4,028 sides. And this gives a perimeter of 4,028 centimeters.

zigzag shape

perimeter calculation

squares

exposed sides

geometry