The diagonal of cube is a line segment that connects two non-adjacent vertices of the cube and passes through its center. In other words, it is a line segment that spans from one corner of the cube to another, passing through the center of the cube.
For a cube with edges of length “a,” the length of the diagonal (d) can be found using the Pythagorean theorem. Since the cube has all sides equal, the diagonal forms a right triangle with two sides of length “a” and the diagonal as the hypotenuse. The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem in this context, we have:
d^2 = a^2 + a^2 + a^2 d^2 = 3a^2
Taking the square root of both sides, we get:
d = √(3a^2) d = a√3
Therefore, the length of the diagonal of a cube with edges of length “a” is given by the formula d = a√3.
Diagonal Calculator
Important Links