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 = a^{2}

Since there are six sides, the total surface area,

TSA = a^{2} + a^{2} + a^{2} + a^{2} + a^{2} + a^{2}

TSA = 6 × a^{2}

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

Surface area = 6 × a^{2}

Surface area = 6 × 3^{2}

Surface area = 6 × 3 × 3

Surface area = 54 cm^{2}