A cube consists of congruent sides and each face of a cube is a square.
The area of a square is a2 and because the cube has six sides, the surface area of the cube is 6 (a2 ) or 6a2
A diagonal on the face of the cube will create two 45-45-90 triangles where the legs = x and the hypotenuse = x√2.
The diagonal d is also the hypotenuse
Solving for x will yield the length of each side .
x = d/√2
x= (d)(√2) / (√2)(√2) = d√2 / 2
To calculate the area of one side, determine x2
(d√2 / 2)2 = 2d2 / 4 = (1/2)d2
The area of 6 side is (6)(1/2)d2 = 3d2 which is the surface area.
SA = 3d2
The volume is a3 or x3 = (d)(√2) / 2 * (d)(√2) / 2 * . (d)(√2) / 2 . = d3 * . 2√2 /8 =
V = d3√ 2 /4
Volume is d cubed multiplied by the square root of 2 divided by 4