如图所示,在梯形ABCD中,AD∥BC,CE是∠BCD的平分线,且CE⊥AB,E为垂足,BE=2AE,若四边形AECD的面积为1,则梯形ABCD的面积为__

（1）∵∠ADC +∠DCB = 180°,∠DCB = 75°
?∴∠ADC = 105°
?∵∠ADC =∠ADE +∠EDC,∠EDC = 60°
?∴∠ADE = 105°-60°= 45°
（2）取DE的中点G,分别连接银,DG
?∵∠EAD = 90°,∠ADE = 45°
?∴△EAD等边三角形
?∴AE = AD
?∴AG⊥DE
?∵△ECD是一个等边三角形
?∴CG⊥DE
?∴点A,G,C三点在同一条直线上
?△ABC∠B = 90°,∠BAC = 45°
∴△ABC是等腰直角三角形?
?∴AB = BC
（3）延长EB至H,使得EB = BH,连接的CH
?∵∠EBC = 90°,∠欧洲央行= 15°
?∴∠ECH = 2∠ECB = 30°,∠HEC =∠EHC = 75°
?∵∠FBC = 30°,∠DCB = 75°
?∴∠BFC = 75°
?∴△ECH△FBC类似
?∴FC/2EB = BC / CE
?∴FC = 2EB * BC / CE = 2 *是* cos15°= 2 * EC * sin15°* cos15°
?∴FC / DC = FC / EC = 2 * sin15°* cos15°= sin30°= 1/2
?∴DF / FC = 1