Question 173
Let $ABCD$ be a convex quadrilateral with area $S$. Let $a = AB$, $b = BC$, $c = CD$ and $d = DA$. For every permutation $x, y, z, t$ of $a, b, c, d$, show that
$$
S \leqslant \frac{1}{2}(xy + zt)
$$
$$
S \leqslant \frac{1}{2}(xy + zt)
$$