To calculate the diagonal of a square, you can use the Pythagorean theorem, which states that the square of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides (the two sides of the square).

So, if “s” is the length of one side of the square, then the diagonal “d” can be calculated as:

d = √(s^2 + s^2) = √(2s^2)

or

d = s√2

Here’s an example: if the length of one side of the square is 6 cm, then the diagonal can be calculated as:

d = 6√2 ≈ 8.485 cm

Therefore, the diagonal of a square with a side length of 6 cm is approximately 8.485 cm.

The steps to calculate the diagonal of a square:

1. Determine the length of one side of the square. Let’s call it “s”.
2. Use the Pythagorean theorem to find the length of the diagonal, which is the hypotenuse of a right triangle. The two legs of the right triangle are the two sides of the square.
3. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In this case, the equation is:

   diagonal^2 = s^2 + s^2

   Simplifying this equation gives:

   diagonal^2 = 2s^2

4. Take the square root of both sides of the equation to solve for the length of the diagonal:

   diagonal = √(2s^2)

   Alternatively, you can simplify this to:

   diagonal = s√2

So, the formula for finding the diagonal of a square is diagonal = s√2, where “s” is the length of one side of the square.

For example, if the length of one side of a square is 10 cm, the diagonal can be calculated as follows:

diagonal = 10√2 ≈ 14.142 cm

Therefore, the diagonal of a square with a side length of 10 cm is approximately 14.142 cm.