Surface area of a cube

A cube, also known as a hexahedron, looks like this:

A cube has six faces. To work out its surface area, we need to find the area of each face and add up all the values. We can start with the face ABCD:

The face is a square, and the area of a square whose side has length a is

$$S_{◻}=a\cdot a=a^2$$

A cube has six such faces – all with the same area – so the surface area of the cube is

$$S=6\cdot a^2$$

For example, if a cube has edge length a = 10, its surface area is

$$S=6\cdot {10}^2=6\cdot 100=600$$

Calculator: work out the surface area of a cube