Diagonal of Square Formula
Before going to know what is the diagonal of a square formula, first, let us recall what is diagonal. A diagonal of a polygon is a line segment that is obtained by joining any two nonadjacent vertices. In the following square, AC and BD are diagonals. The diagonal of square formula is derived using the Pythagoras theorem. Let us understand how to derive the formula to find the diagonal of a square.
What Is the Diagonal of Square Formula?
In a square, the lengths of both the diagonals are the same. The length of a diagonal, d of a square of side length 'x' is calculated using the Pythagoras theorem. Here consider the triangle ADC within the square.
Using Pythagoras theorem,
\[ \begin{aligned} d &= \sqrt{x^2+x^2}\\[0.2cm]&= \sqrt{2x^2}\\[0.2cm]&= \sqrt{2} \cdot \sqrt{x^2}\\[0.2cm] &=\sqrt{2}\,\,x \end{aligned} \]
Thus, the diagonal of a square formula is:
d = x √2
Let us check a few examples to understand how to find diagonal of square formula.
Solved Examples on Diagonal of Square Formula

Example 1: Find the length of each diagonal of a square of side 14 units. Round your answer to the nearest tenths.
Solution:
To find: The diagonal of a square of side 14 units.
The side length of the square is, x = 14 units.
By the diagonal of a square formula, the length of the diagonal, d is:
d = x √2
d = 14 √2 (or) 19.8 units
Answer: The length of each diagonal of the given square = 14 √2 (or) 19.8 units.

Example 2: Find the side length of a square whose diagonal length is 3√2 units.
Solution:
To find: The side length of the square whose diagonal is d = 3√2 units.
Let us assume the side length of the square is x units.
By the diagonal of a square formula, the length of the diagonal, d is:
d = x √2
3√2 = x √2
3 = x
Answer: The side length of the given square = 3 units.