Cubes are one of the simplest three-dimensional shapes. You're familiar with ice cubes, square cartons, square boxes -- these shapes are all cubes. A cube has six square sides of equal area. As long as you know the length of one of the sides of the cube -- you can calculate the cube's lateral area and the surface area of any cube.

### Lateral Area

**A three-dimensional shape's lateral area is the area around the side of a shape -- not including that shape's top or bottom.**

A cube has six square sides.

Two of these sides are the top and bottom -- but you don't count the top and bottom sides in the lateral area. So the cube's lateral area is equal to the area of four squares.

A square's area is equal to the length of its sides, *s,* multiplied by itself, or *squared*. This is written as *s^2.* The exponent *2* shows how many times you multiply s by itself.

So:

**s^2 = s x s**

Since the area of a square is s^2, and the lateral area, *L,* of a cube is the area of four squares, then:

**L = 4 x s^2, or 4 x s x s**

So, if the length of one of the cube's sides is *3* inches, you could solve for lateral area by multiplying *4 by 3 by 3:*

**L = 4 x 3 inches x 3 inches** or *3 x 3 = 9; 4 x 9 = 36* **L = 36 square inches**

So the cube has a *lateral area* of 36 square inches.

### Surface Area

**A cube's surface area includes the area of the cube's top and bottom.** Since a cube has six square sides, the surface area --

*SA*-- is equal to 6 times the area of a square, s^2:

**SA = 6 x s^2, or 6 x s x s**

Suppose the length of one of the cube's sides is 4 inches. You can solve for *surface area* by multiplying *4 by 4 by 6:*

**SA = 6 x 4 inches x 4 inches** or *4 x 4 = 16; 6 x 16 = 96* **SA = 96 square inches**

So, the cube has a *surface area* of 96 square inches.