Area of parallelogram = Area of square. Shear transform Below the parallelogram is obtained from square by stretching the top side while fixing the bottom.
Since area of parallelogram is base times height, both square and parallelogram have the same area.



This is true no matter how far I stretch the top side.



In below figure it is easy to see why both areas are same.


But it's not that obvious in first two figures. Any help seeing why the area doesn't change in first figure?
Behold, $\phantom{proof without words}$
A kite is flying into the sky!



In fact, it is what you and Stijn already observed. This drawing summarizes it.