Covering any rectangle with this shape is not possible

Question

Why can I not tile any rectangle without gaps with the given shape?

https://i.stack.imgur.com/9oxO4.png

You can mirror the shape (i.e. turn it around an axis in its own plane by $\pi$).

Answer 1

In the picture below, you can see that we've placed the red tile in the only place that any tile can go in order to fill the bottom left corner of the rectangle. We have then placed the blue tile in the only place that any tile can go in order to fill the square which is directly below the green frame. Now notice that there is no way to place a tile so that the green frame is filled without overlapping tiles.