Practical Geometry

How to Calculate Diagonal Distance Between Corners of a Square?

Diagonal of Square Formula

One of the basic shapes that we learn in the introduction of shape is square. In addition, we found this common shape almost everywhere we go. Moreover, the windows of the houses are mostly square in shape. In this topic, we will discuss the diagonal of square formula that will help us to understand how to calculate the diagonal distance between the corners of a square.

What is Diagonal?

Diagonal is the slant line that passes through opposite corners of a square. Moreover, a diagonal divides the square into two triangles.

Furthermore, the diagonal of the square always make an angle of 45o. In addition, the diagonal of a square is the square root of twice the square of the side.

In simple words, the length of a diagonal is equal to the length of a side multiplied by the square root of 2 that is 1.414.

diagonal of square formula

Example: Suppose the side of square measures 13 cm then its diagonal will be

d = s√2

Diagonal = Side × square root of 2

Putting value in the formula we get

Diagonal = 13 × 1.414 = 18.38 cm

Ways to Calculate Diagonal of Square Formula

There are three methods by which we can calculate the diagonal of a square. Besides, these three methods use different techniques for finding the diagonal of the square.

Method 1: If the length of one side is known

For finding the diagonal of a square using this method we simply need to follow some simple rule. Firstly, find the length of one side by measuring it. After that, put the value in the formula d = s√2.

Furthermore, in the next step put the value of side (s) in the formula that you find in the first step. Finally, solve the equation to know the length of the diagonal of the square.

Method 2: By knowing the perimeter

If the perimeter of the square is given then you can easily find the length of the diagonal by following the simple steps. First of all, you know that the formula of the perimeter is 4s (Perimeter of Square = 4 × side).

So, by using this formula find out the length of a side and then apply it in the formula d = s√2 and you will get the length of diagonal of a square.

Method 3: The area of the square

We know that the area of a square is s2 (Area of Square = s2). So, we can get the value of the side by reversing the formula of area of the square. In addition, after knowing the value of the side put the value of side in the formula for calculating diagonal that is d = s√2.

Properties of the Diagonal of a Square

  • The diagonal of the square divides it into 2 congruent isosceles triangles.
  • Furthermore, they make an angle of 45o at the point they meet with the corner of the square.
  • Also, the triangle that forms from the joining of diagonal is a right-angle triangle.
  • The two sides of the square that form the triangle after joining of diagonal are equal in length.
  • Moreover, the sum of the angles of the triangle form is 180o.
  • The length of the diagonal can also be found with the help of Pythagoras theorem.

Solved Question for You

Question. Find the length of two diagonal of two squares A if the perimeter of the square is 60.

Answer. Square A

Formula of perimeter of square = 4 × side = 4s

Then 60 = 4s

s = 60 ÷ 4 = 15

Putting the value of s into the formula of diagonal

Diagonal = s√2

d = 15√2

d = 15 × 1.414 = 21.21

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