ABCD is a convex quadrilateral. The points P, Q, R and S are the midpoints of the edges of ABCD. You can change the shape of the quadrilateral ABCD.

What do you notice about the quadrilateral PQRS as ABCD changes?

Is the area of PQRS always the same fraction of the area of ABCD and, if so, what is this fraction?

Try to prove your conjectures.