Problem
Figures 1, 2, 3 have sides 1, 2, 3 cm - figure n's side is n cm, so figure 4 has side 4 cm.
Spotting that the side grows by 1 cm each step is the Grade 4 idea of generating a shape pattern from a rule.
4.OA.C.5Look For A PatternCheck small cases: figure 1 = 4 cm, figure 2 = 8 cm, figure 3 = 12 cm - perimeter is always 4 times the side.
Working the small figures first shows the simple 'four equal sides' perimeter rule before jumping to figure 4.
3.MD.D.8Solve An Easier Related ProblemA square's perimeter equals four times the length of one side.
The perimeter is the whole distance around the square, and that boundary is exactly its four sides laid end to end with no gap or overlap.
Cutting the boundary into its four sides leaves no piece out and doubles no piece, so the four side lengths add back up to the full perimeter.
All four sides of a square are the same length, so adding the four sides is just adding one side length four times.
Adding the same length four times is the same as taking four equal groups of it, which is four times one side.
The fourth figure is a 4 cm by 4 cm square, so its perimeter is 4 times 4 cm.
Multiplying side by 4 for a square's perimeter is a basic Grade 4 rectangle-perimeter formula.
4.MD.A.3Draw A DiagramFigure number tells you the side in cm, and a square's perimeter is just 4 times its side - so figure 4 is 4 x 4 = 16 cm!