The perimeter of a shape tells us the combined length of all of the sides of that shape. We can use a coordinate grid to help us find the length of each side of a shape and then add those together to find the perimeter.

As an example, let's look at this square here. The question asks, “How long is one side of the square, and what is the perimeter of the square?” So let's begin by finding the length of each side. To do that, let's pick two adjacent corners on this square. We can pick this one here, and this one here. We can use the coordinates of each of these corners to tell us how far they are apart, so to get from an x-coordinate of 4 to an x-coordinate of 9, this must have a length of 5. You could also count the distance in boxes, which is 1, 2, 3, 4, 5. Now, because this is a square, every single side should have the same length, but let's check one other side just to be sure. Let's check the distance from here to here. Here we're going from a y- coordinate of 10 to a y-coordinate of 5. To go from 10 to 5, this again must have a length of 5, which we could check as 1, 2, 3, 4, and 5. So each side has a length of five units. The perimeter is going to be equal to 5 plus 5 plus 5 plus 5, because there are 4 sides of length 5 on this square. 5 plus 5 plus 5 plus 5 equals 20, so this shape has a perimeter of 20 units. Let's look at one more example.

This one reads, “The longest side of the right triangle is 7.8 units long. What are the lengths of the height and base of the right triangle? What is the perimeter of the right triangle?” Well, first let's find the length of the height. Here we're going from a coordinate of (-9, 5) to a coordinate pair of negative (9, 10), So the x-coordinate doesn't change but the y-coordinate increases from 5 to 10, which is a change of 5, and we can count that off 1, 2, 3, 4, 5. So the height of this triangle is 5 units. Now let's find the length of the base. For the base we go from a coordinate pair of (-9, 5) to (-3, 5). So while the y- coordinate stays the same at 5, the x-coordinate increases from negative 9 to negative 3, which is a change of 6. We can count off again 1, 2, 3, 4, 5, 6, so that confirms this length of 6 units. The if longest side of this triangle has a length of 7.8 units, then the perimeter is equal to 5 plus 6 plus 7.8. 5 plus 6 plus 7.8 is 18.8 units.