Lateral Area of a Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube can also be called a regular hexahedron and is one of the five Platonic solids. It is a special kind of square prism, of rectangular parallelepiped and of trigonal trapezohedron. (Source: From Wikipedia).

Here we are going to learn how to calculate the lateral area of a cube.

 

Formula to Find the Lateral Area of a Cube

 

We know that a cube is a solid bounded by six square faces. the total surface area of a cube is the sum of areas of all square faces.The lateral area means the surface area of the cube without the area of the top and bottom square faces.The unit used to measure the lateral area of a cube is square units.

So the lateral area of a cube = 4(area of square) square units

                                                    = 4(a2) square units

                                                    = 4a2 square units

 

Example Problems to Find the Lateral Area of a Cube

 

Example 1

Find the lateral area of cube with side length 4 meter.

Solution

The lateral area of a cube = 4a2 square units

Given, a = 4

So, the lateral area of the given cube = 4 * 42

                                                                   = 4* 4* 4

                                                                   = 64

The lateral area of the given cube is 64 square meter.

Example 2

Find the lateral area of cube whose side length is 3 feet.

Solution

The lateral area of a cube = 4a2 square units

Given, a = 3

So, the lateral area of the given cube = 4 * 32

                                                                   = 4 * 3 * 3

                                                                   = 36

The lateral area of the given cube is 36 square feet.

 

Example 3

The volume of a cube is 125 cubic feet, find its lateral area

Solution

The volume of a cube = a3 = 125

Taking cubic root on both sides,

                                             a = 5

So, the side of the cube = 5

The lateral area of a cube = 4a2 square units

                                                = 4 * 5 * 5

                                                = 100

So, the lateral area of the given cube is 100 square feet.