The diagonal of the cube is 12√3, determine the full surface of the cube.

Let us denote by variable n the length of the side of this geometric figure.

Therefore, using the formula from the Pythagorean theorem, we get the following equation:

n ^ 2 + n ^ 2 = (12√3) ^ 2;

2n ^ 2 = 144 * 3;

n ^ 2 = 216.

In turn, we can represent the full surface of this geometric figure in the form:

6n ^ 2.

Substitute the value n ^ 2 from the equation above and calculate what the full surface of this geometric figure will equal:

6 * 216 = 1296.

Answer: The full surface of a cube is 1296 conventional units.