A rectangular paper, folded into two congruent parts, has a perimeter of 34 cm for each part when folded along one set of sides, and 38 cm when folded along the other set. What is the area of the paper (sq. cm)?
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Folding a paper of side $x$ and $y$ results in a new perimeter of $2(x/2 + y)$ or $2(x + y/2)$.