Which expression gives the total surface area of a cube with side length 'a'?

To determine the total surface area of a cube, it's important to recognize that a cube consists of six identical square faces. The area of one square face can be calculated using the formula for the area of a square, which is side length squared. In this case, since each side of the cube is of length 'a,' the area of one face is a².

Since there are six identical faces on the cube, you would multiply the area of one face by the total number of faces. Therefore, the total surface area of the cube can be calculated as follows:

Total Surface Area = 6 × area of one face = 6 × a² = 6a².

This leads us to the conclusion that the expression for the total surface area of the cube with side length 'a' is 6a². This matches with the correct choice, which reflects the mathematical principle behind calculating the surface area of three-dimensional shapes like cubes.