A parallelogram will have, like a rectangle, two pairs of parallel lines (the lines in one pair are exactly the same length, however aren't the same as the other pair), just as a rectangle has.
If the sides are the same on both shapes, the area will remain the same
The formula for the area remains the same - LxW (L being one side, not the length of the entire shape)
⇒2 Pairs of parallel lines
⇒Same formula
⇒Parallel lines are the same length
⇒Same Area*