# Area Of A Square

## What is the formula for calculating the area of a square?

A square is a flat shape having  4 equal sides and all four right angles.  In a square, all the sides have equal lengths and each of the internal angles is 90°. Also, the opposite sides are said to parallel, meaning that a square is a parallelogram. Sometimes, a square may fit the definition of a rectangle where all sides are 90° and a rhombus where all sides have equal lengths.

### This is how a square looks like: It’s easy to find the area of a square if you are given the length of the side, the perimeter, or the diagonal. There are different ways to do and they include:

### Use of the Length of One Side

Let’s say that you are given a square having a side length of 3 cm. What you need is to write down the formula for finding the area.

Area = s2 where s is the length of the side. In a square we know that all sides have equal lengths. So in calculating the area, you square the length of the side.

Area = 32

Area = 3 x 3

Area = 9 cm2

Remember that squaring the side is just the same as taking the base and multiplying it by the height of the square.

### Use of a Known Diagonal

When you are not given the length of the side, but have the diagonal, you can still find the area of the square. In this case, you will apply the Pythagorean Theorem. The reason you use this formula is because when you draw a line running between the opposite vertices, you have two triangles formed. The Pythagorean Theorem is used to find the hypotenuse or the longest side of a right angled triangle.

Let’s take the diagonal to be 10 cm. In this case, we have been given the hypotenuse of the triangle created when we run a line dissecting the square through opposite vertices.

Pythagorean Theorem states that a2 + b2 = c2

But since in a square, the a and b are equal in lengths, we call them s. In this example, c stands for the hypotenuse.

Therefore if we replace a and b for s, we shall have an equation like this:

s2 + s2 = c2

2s2 = c2

2s2 = 102

This is because we have been given the diagonal or hypotenuse as 10cm.

What we want to find is the length of one side, so that you calculate the area of the square.

2s2 = 100

s2  = 50

s = √50

s = 7.07 cm

Now that we have found the length of one side, we can use that to calculate the area of the square.

Area = s2

Area = 7.072

Area = 50 cm2

## You are Given The Perimeter

When the perimeter is provided, what you want to do is find the length of the side. Because we said that a square has equal lengths, you will divide the perimeter by 4. The reason is that there are four sides that add up to make the perimeter.

Let’s say that you are given the perimeter of a square as 48 cm. What you do is divide 48 by 4

So,  s = 48/4 where s represents the value of the side

Therefore s= 12 cm

Now that you have got the length of the side, what you need is to square it to find the area of the square.

Area = s2

Area = 122

Area = 144 cm2