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Surface area of a cubeTo derive the formula of the surface area of a cube, 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 = a2 Since there are six sides, the total surface area, call it SA is: SA = a2 + a2 + a2 + a2 + a2 + a2 SA = 6 × a2 Example #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 Example #2: Find the surface area if the length of one side is 5 cm Surface area = 6 × a2 Surface area = 6 × 42 Surface area = 6 × 4 × 4 Surface area = 96 cm2 Example #3: Find the surface area if the length of one side is 1/2 cm Surface area = 6 × a2 Surface area = 6 × (1/2)2 Surface area = 6 × 1/2 × 1/2 Surface area = 6 × 1/4 Surface area = 6/4 cm2 Surface area = 3/2 cm2 Surface area = 1.5 cm2
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