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Let's start by finding the length of the edge of the initial cube. A cube has 6 different surfaces that are all squares that have the same length and widths and so have the same areas. The surface area of the cube must be 6 * the area of one square because there are six surfaces. As an equation, if S is surface area and a is area of one square: s=6a.
We know that s=24 cm^2 for the initial cube. Putting that in to the equation,
Now we know the area of one square to be 4 cm^2. If the area of the square is 4 cm^2, the length of one side must be 2 since the area of a square is the length squared. a=l^2
If the initial length is 2, tripling it gives a square with length 6. The area of a square with length 6 is 6^2 or 36. The surface area of the cube made up of such squares is 6*36 or 216.