CWMO 2015 Problem 5

Let $a,b,c,d$ are lengths of the sides of a convex quadrangle with the area equal to $S$ , set $S =\{x_1, x_2,x_3,x_4\}$ consists of permutations $x_i$ of $(a, b, c, d)$ . Prove that $$S \leq \frac{1}{2}(x_1x_2+x_3x_4).$$