A parallelogram has both diagonals and both mid-lines (each parallel to a pair of sides) drawn. How many parallelograms are there in the figure?

The mid-lines make 4 small parallelograms, 2 upper/lower halves, 2 left/right halves and the whole: $4+2+2+1=9$. The diagonals only cut pieces into triangles and add no new parallelogram.