Question: how do you work out the diameter of a square?
Answer: As we noticed before, the diagonal of a square divides the square into two congruent right triangles.
Legs are square sides and the length of diagonal of the square is the hypotenuse. Given the side length of the square: a² + a² = diagonal² diagonal = √(a² + a²) = √(2 * a²) which simplifies to. diagonal = a√2.