Let $AB$ and $DC$ intersect at $E$. $\angle E=30$ Let $DF$ and $BG$ are altitudes of $ADB$ and $DBC$ As $\angle EBC>30,\angle ECB>30$ then $BC<EB$ and $BC<EC$. Also $DF=\frac{1}{2}DE,BG=\frac{1}{2}BE$ $S(ABCD)=\frac{DF*AB+CD*BH}{2}=\frac{DE*AB+CD*BH}{4}=\frac{CD*AB+CE*AB+CD*BH}{4}>\frac{AB*CD+AB*BC+CD*BC}{4}$