How to Find the Area and Perimeter of a Square
Area is how much covers a shape or fills a shape in, while perimeter is the distance around a shape. The area of a square is found by taking one of the side lengths and squaring it. The reason for that is that all the sides of the square are the same. If you just take one side length and square it, then you can find the area of the square.
The perimeter of a square is found by multiplying 4 times the side length, because again the perimeter is distance around and you have four sides that are all the same length. Instead of doing side plus side plus side plus side, you can just multiply four times s or 4 times side length to find perimeter. Let’s look at an example.
Area
What is the area and perimeter of a square with side length 3 in? This side length of 3 inches right here, that’s our s in both of our formulas. They’ve asked us to find area and perimeter. Let’s start with area. First, we need to write down the formula. A = S2. Then we’ll take our side length and substitute it for s.
A = (3 in)2
A = 9 in2
Our area is 9 in2.
Perimeter
We start with our formula, the perimeter of a square is 4 times the side length. P = 4s. The perimeter is, and again we’re going to substitute our side length for s. P = 4(3in) = 12 in.
You can verify this on your shape, for instance if we took our square and we said our side length was 3. If we split this into 3 both ways, because all our sides are congruent, you can see then with a side length of 3, that our square would be filled with 9 squares, 9 in2. The distance all the way around would be 12 inches.