The sum of all the edges of a cube is 45.6 cm. Find the area of one of its faces.

1) The face of a cube is a square. The area of a square is equal to the square of the length of its side:

S = a * a,

where a is the length of the side of the side face (edge) of the cube.

2) The sum of all the edges of the cube is 45.6 cm = 45.6 * 0.01 m = 0.456 m. The cube has 12 edges in total. Then the length of one side edge is

a = 0.456 / 12 = 0.038 m.

3) Then the area of the side face of the cube is

S = 0.038 * 0.038 = 0.001444 m ^ 2 = 14.44 cm ^ 2.

Answer: S = 14.44 cm ^ 2.