Find the surface area of a cube if the area of its diagonal section is 16 cm2.

Let the side of the cube be equal to a, then the area of the diagonal section is equal to:

a * b = 16, where b ^ 2 = a ^ 2 + a ^ 2,

b = √ (2a ^ 2) = a√2,

a * b = 16,

a * a√2 = 16,

a = √ (16: √2),

The area of the entire surface of a cube is equal to six surfaces:

S1 = a ^ 2,

S = a ^ 2 + a ^ 2 + a ^ 2 + a ^ 2 + a ^ 2 + a ^ 2,

S = 6 * a ^ 2,

S = 6 * (√ (16: √2)) ^ 2,

S = 6 * (16: √2),

S = 6 * 16: √2,

S = 3 * √2 * √2 * 16: √2,

S = 3 * √2 * 16,

S = 3 * 16 * √2,

S = 48√2,