# Formula for finding Diagonal of a square

We know what is a square in geometry and its properties. For finding area of square and perimeter of square we have formulas. When comes to diagonal of a square, does it has any formula? Yes it has the formula. Now we will see what is that formula for finding diagonal of a square. First let us define a square. A quadrilateral which has all the sides equal and each angle is equal to 90 degrees is called square. A square contains two diagonals which are equal in length. Now in this concept we are going to learn how we can find diagonal of a square. So know the formula for length of diagonal of a square and also its proof that means how we got that formula.

## Diagonal of a square formula:

Let PQRS be a square with ‘S ‘units as side. PR is the diagonal in the above diagram.

Therefore, the diagonal PQ is given by  $\sqrt { 2 }$ S units. Square root 2 value just take approximate value i.e. 1.414.

### Proof for diagonal of a square formula: PQR is a right angled triangle.

We know that according to right angled triangle hypotenuse square is equal to sum of squares of remaining two sides. Therefore, the diagonal of square is $\sqrt { 2 }$ S units. 