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.
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)
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.