Area = Length x Width (A = LW) Since the length and width of a square are the same, you can use Area = Length2 (A = L2)
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Use squares and try it out for yourself. Get a number of squares and make a rectangle 3 squares long by 4 squares wide. Count the squares. You should have 12 squares (or 3*4). That's the best way I know to prove the formula.
The cube is bounded by six equal-sized squares, so the surface area is simply six times one of those squares.
Just add the area of the six squares - that gives you 6a2, where a is the length of one side.
The cube's surface area consists of six squares; you can simply add the area of each of the squares. Note that each of the squares has the same size.
The formula is: A2 - B2 = (A + B) (A - B)