The edge of the cube is 10cm, Calculate the surface area of the cube.

The problem is given a cube ABCDA1B1C1D1. By definition, all edges of a cube are equal. Let us denote the length of the edge by a. By the condition of the problem:

a = 10 cm;

The task requires to find the surface area of ​​a cube.

Formula for surface area
The cube has six faces. In our case, these are:

lower base ABCD;
upper base A1B1C1D1;
four side faces AA1B1B; BB1C1C; CC1D1D; DD1A1A.
The surface area (or total surface area) of a cube is the sum of the areas of all six faces. In a cube, all faces are squares.

The base areas are the same:

S1 = | AB | * | BC | = | A1B1 | * | B1C1 | = a ^ 2;

Areas of all side faces AA1B1B; CC1D1D; BB1C1C and DD1A1A are the same and equal:

S2 = | AB | * | AA1 | = | CD | * | CC1 | = | BC | * | BB1 | = | AD | * | AA1 | = a ^ 2;

The lateral surface area is:

Side = 4 * S2 = 4 * a ^ 2;

The total surface area is:

S = 2 * S1 + S side = 2 * a ^ 2 + 4 * a ^ 2 = 6 * a ^ 2;

Calculating surface area
Substitute the original value for a into the resulting formula:

S = 6 * a ^ 2 = 6 * 10 ^ 2 = 600 (cm ^ 2);

Note that the areas of all faces are the same and equal:

a ^ 2 = 10 ^ 2 = 100 (cm ^ 2);

Answer: the surface area of ​​a cube is 600 cm ^ 2