Consider any convex quadrilateral $Q$ made from four rigid rods
  with flexible joints at the vertices so that the shape of $Q$ can
  be changed while keeping the lengths of the sides constant. If
  the diagonals of the quadrilateral cross at an angle $\theta$ in
  the range $(0 \leq \theta < \pi/2)$, as we deform $Q$, the
  angle $\theta$ and the lengths of the diagonals will change.
  <br />

  <div>
    Using the results of the two problems on quadrilaterals
    <a href="http://nrich.maths.org/public/viewer.php?obj_id=437&amp;part=index">
    Diagonals for Area</a> and <a href=
    "http://nrich.maths.org/public/viewer.php?obj_id=439&amp;part=index">
    Flexi Quads</a> prove that the area of $Q$ is proportional to
    $\tan\theta$.
  </div><br />