Question

梯行abcd,ad平行于bc,bc=4,ad=1,ac=3,bd=4,则梯行abcd的面积=?

Answer 1

过A作AEIIBD交CB的延长线于E

∵AD平行于BC AEIIBD

∴ADBE是平行四边形

∴AD=BE=1 AE=BD=4

且S△AEB=S△ABD

∵S△ABD=S△ACD(同底等高)

∴S△AEB=S△ACD

∴梯形ABCD的面积=S△ABC+S△ADC=S△ABC+S△ABE=S△AEC

∵EC=EB+BC=1+4=5 AE=4 AC=3

∴EC^2=AE^2+AC^2

∴△AEC是直角三角形

∴梯形ABCD的面积=S△AEC=(1/2)AE*AC=(1/2)*4*3=6