The formula for the area of a square with given side length  is . Since the area  of the square  is  square units, its side length  can be computed as follows:

.

The formula for the perimeter of a square with given side length  is . The side length  of square  has already been calculated, so we can substitute in this value for  in this formula to deduce its perimeter.

.

Hence, the perimeter of the square  is  units.

First we need to find the measure of one side. Since formula for area of a square is 

we can plug in area and find side 

we have to take the square root of each side to solve for S 

so 

.

Now that we have our side we can solve for perimeter. The formula for perimeter of a square is 

 or  

Since we know S=12 we multiply 12 x 4 and we get 48.

The area of a square is:

, where s is the side length of the square.

So using the numbers:

Therefore, every side of the square is 25.

Now to find the perimeter, a square has 4 equal sides:

The perimeter of the square is 100

The sides can be found by taking the square root of the area.

, where = side.

. 

So the length of a side is 6.3 cm.

First, know that all the side lengths of a square are equal. Second, know that the sum of all 4 side lengths gives us the perimeter.  Thus, the square perimeter of 16 is written as

where S is the side length of a square. Solve for this S

So the length of each side of this square is 4.

We will have two formulas to help us solve this problem, the area and perimeter of a square.

The area of a square is:

 ,

where length of the square and width of the square.

The perimeter of a square is:

Plugging in our values, we have:

 Since all sides of a square have the same value, we can replace all and with (side). Our equations become:

Therefore, .

The area of any quadrilateral can be determined by multiplying the length of its base by its height.

Since we know the shape here is square, we know that all sides are of equal length. From this we can work backwards by taking the square root of the area to find the length of one side.

The length of one (and each) side of this square is 6 inches.

One of the necessary conditions of a square is that all sides be of equal length. Therefore, because we are given the length of one side we know the length of all sides and that includes the length of the opposite side. Since the length of one of the sides is 4 we can conclude that all of the sides are 4, meaning the opposite side has a length of 4.

We begin by recalling the formulas for the perimeter and area of a square respectively.

Using these formulas and the fact that the perimeter is half the area, we can create an equation.

We can multiply both sides by 2 to eliminate the fraction.

To get one side of the equation equal to zero, we will move everything to the right side.

Next we can factor.

Setting each factor equal to zero provides two potential solutions.

       or        

However, since a square cannot have a side of length 0, 8 is our only answer.