A cube is a simple shape, and it would make sense to assume there is a simple formula for computing its surface area. All sides of a cube have the same length, and all the faces have the same area. Since a cube has six faces, all you have to do is calculate the area of one face and multiply by 6 to find the total surface area. The mathematical formula that results from this discussion is: For a cube with sides of length L, the surface area **A = 6L ^{2}**.

## Area of a Square

A cube is made from squares, and a square is a special type of rectangle. You find the area of any rectangle by multiplying the length of its longer side by that of its shorter side. When the rectangle becomes a square, all four sides have the same length, so you simply multiply the length by itself. In other words, you square the length: **L ⋅ L = L ^{2}**.

## Surface Area of a Cube

The surface area of a cube can be a useful thing to know. For example, someone designing a 3-D solar collector needs to know how many solar cells will fit on its surface. The answer depends on surface area.

## Sciencing Video Vault

To find surface area, first compute the area of one face, which is simply L^{2}. The total surface area is the area of all six faces, so that would be 6L^{2}.

## Example

**One die from a pair of dice is half an inch high. What is its surface area?**

Dice are cubic, so first find the area of one face. You know the side of one face is 0.5 inches, so 0.5^{2} = 0.25. There are six faces on the die, so multiply that area (0.25) by 6 to get the surface area of the cube:

Surface area A = 6(0.25) = 1.5 square inches