How to Calculate the Diagonal of a Square Using the Pythagorean Theorem
Learn how to find the diagonal of a square with a simple formula based on the Pythagorean theorem. Easy step-by-step calculation explained.
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The diagonal of a square can be calculated using the formula d = a√2, where a is the length of one side of the square. This formula derives from the Pythagorean theorem, applying to the right triangle formed by the square's diagonal and two of its sides. Simply multiply the length of one side by the square root of two to find the diagonal length.
FAQs & Answers
- What is the formula to calculate the diagonal of a square? The diagonal of a square is calculated using the formula d = a × √2, where 'a' represents the length of one side of the square.
- Why does the diagonal of a square involve the square root of 2? Because the diagonal forms the hypotenuse of a right triangle with the two sides of the square, and by the Pythagorean theorem, its length is the side length multiplied by the square root of 2.
- How can I find the diagonal if I only know the square’s perimeter? First, find the side length by dividing the perimeter by 4, then multiply that length by the square root of 2 to get the diagonal.