Only the top and bottom sides change each time. The left and right edges stay the same.
Number of Squares
Perimeter
1
4
2
6
3
8
4
10
10
22
30
62
n
2n+2
Practice makes perfect
Let's take a look at the given figures.
When there is only 1 square, we can count the number of sides to determine that the perimeter is 4. Similarly, when there are 2 squares, we can determine the perimeter by counting. Therefore, we can fill in the first empty space in the table by counting the sides of the figure with 3 adjacent squares.
Number of squares n
Perimeter p
1
4
2
6
3
8
4
?
10
?
?
62
n
?
The pattern we see is that for each square added to the figure, the perimeter p of the figure increases by 2. Does the relationship p=2n adequately describe the pattern? Let's test it with the first figure.
We are definitely missing something in the equation. When counting the sides each time, did you notice that only the top and bottom sides change when the number of boxes changes? The number of sides on the left and right of the figure is a constant 2. By adding 2 to the expression for p, our equation will satisfy the pattern.
p=2n+2
Let's use this equation to fill in the rest of the table.
