过A作AE⊥BC于E,过D作DF⊥BC于F,则
∵∠B=60°,∠C=30°,AD‖BC
∴BE=AE/√3,AB=2*BE=2*AE/√3,CF=√3*DF,CD=2*DF
∵AD=EF,AE=DF,AD=1,BC=5
∴BC
=BE+EF+CF
=AE/√3 +1 +√3*AE
=AE*(√3 +1/√3) +1
=5
∴AE=√3
∴AB=2,CD=2√3
∴梯形面积S=(AD+BC)*AE/2=(1+5)*√3/2=3√3