I guess it depends on the kind of shoe box. Let's take a regular shoe box with six rectangular sides. Let the dimensions be a x b x c The surface area is 2(ab + ac + bc) Intuitively, you have three different dimensions, a, b, and c. So each panel has area of ab, ac, or bc. Then if you look at opposite sides of the box, you see two opposite sides are the same, so you multiply the sum by two.
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