A pyramid \( PABCD \) has a rectangular base \( ABCD \) where \( AB = 12 \) and \( BC = 5 \). The apex \( P \) is directly above the center of the rectangle, and the perpendicular height from \( P \) to the base \( ABCD \) is 10 units. Calculate the surface area of the pyramid. Let's think step by step and output the final answer within \boxed{}.
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