The midpoints of the sides of an arbitrary quadrangle form a parallelogram. If the quadrangle is convex or reentrant, i.e. not a crossing quadrangle, then the area of the parallelogram is half as big as the area of the quadrangle. http://en.wikipedia.org/wiki/Varignon%27s_theorem
Start animation to change the size/shape of quadrilateral and check areas of quadrilateral and parallelgram