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16 sq cm.

Suppose the original square had sides of x cm. Then the folded rectangle has pairs of sides of length x and x/2 cm. The perimeter is 2(x + x/2) = 3x.

So 3x = 12 so that x = 4 and the area of the original square, with sides of 4 cm is 16 sq cm.

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Q: What is the area of the original square if a square piece of paper is folded in half vertically and the resulting figure has a perimeter of 12 cm?
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