Is the diagonal of a square equal to its sides?

A square is a closed two-dimensional figure with four sides and four corners. The length of all four sides is equal and angles at the corners are right-angles.

Answer: No, the diagonal of a square is not equal to its sides.

The diagonal of a square is calculated by using the formula: Diagonal of Square (d) = √2 × s, Here 's' is the side of the square.

Explanation:

The following image shows a square ABCD with diagonals, AC and BD

The diagonal formula is calculated by using the Pythagoras Theorem.

Consider a square ABCD with sides AB = BC = CD = AD = s and diagonals AC = BD = d. Since the angles at the corners of the square are right angles, we have

AC² = AD² + CD²

d² = (s² + s²)

    = 2s²

d = √2 × s

So, Diagonal of Square (d) = √2 × s, where s is the length of each side of the square.

Therefore, the diagonal of a square is not equal to its sides.