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.
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.
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.
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.