Surface Area Of Cube

 

Let’s derive the formula of the surface area of a cube, we will need to start with a cube as shown below and call the length of one side a.

             (fig I)

We shall use a cube template as shown in the figure below (fig II) to form a cube as seen in the figure above (fig I)

                         (fig II)

When we see the cube template we understand that cube has six sides and each side is a square,
The area of one square is a × a = a2
Since there are six sides, the total surface area,
TSA = a2 + a2 + a2 + a2 + a2 + a2
TSA = 6 × a2   

DEMONSTRATION:

1) Find the surface area if the length of one side is 3 cm.

Surface area = 6 × a2 
Surface area = 6 × 32 
Surface area = 6 × 3 × 3 
Surface area = 54 cm2