The diagonal of a cube is 5√3, find its total surface area.

According to the formula, the diagonal of the cube is equal to the product of the edge of the cube (a) by the square root of three, we find from it the length of the edge of the cube.

d = a√3.

5√3 = a√3;
a = 5.

Let’s find the area of one of the 6 identical faces of the cube.

Sg = 5 * 5 = 25.

Let’s find the total surface area of the cube.

Spov = 6 * 25 = 150 units 2.

Answer: total surface area 150 units 2.