CRUZ C. answered • 04/29/19

Experienced Math Dept Chair, 7+ Years of Teaching Experience

A cube consists of congruent sides and each face of a cube is a square.

The area of a square is a^{2 } and because the cube has six sides, the surface area of the cube is 6 (a^{2} ) or 6a^{2}

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

d=x√2

Solving for x will yield the length of each side .

d/√2=x√2/√2

x = d/√2

x= (d)(√2) / (√2)(√2) = d√2 / 2

To calculate the area of one side, determine x^{2}

(d√2 / 2)^{2} = 2d^{2} / 4 = (1/2)d^{2}

The area of 6 side is (6)(1/2)d^{2} = 3d^{2} which is the surface area.

SA = 3d^{2}

The volume is a^{3} or x^{3} = (d)(√2) / 2 * (d)(√2) / 2 * . (d)(√2) / 2 . = d^{3} * . 2√2 /8 =

V = d^{3}√ 2 /4

Volume is d cubed multiplied by the square root of 2 divided by 4