Surface area of a cube
To derive the formula of the surface area of a cube, do the followings:
Start with a cube as shown below and call the length of one side a:
In order to make a cube like the one shown above, you basically use the following cube template:
Looking at the cube template, it is easy to see that the 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, call it SA is:
SA = a
^{2} + a
^{2} + a
^{2} + a
^{2} + a
^{2} + a
^{2}
SA = 6 × a
^{2}
Example #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}
Example #2:
Find the surface area if the length of one side is 5 cm
Surface area = 6 × a
^{2}
Surface area = 6 × 5
^{2}
Surface area = 6 × 5 × 5
Surface area = 150 cm
^{2}
Example #3:
Find the surface area if the length of one side is 1/2 cm
Surface area = 6 × a
^{2}
Surface area = 6 × (1/2)
^{2}
Surface area = 6 × 1/2 × 1/2
Surface area = 6 × 1/4
Surface area = 6/4 cm
^{2}
Surface area = 3/2 cm
^{2}
Surface area = 1.5 cm
^{2}