延长AF、BC相交于点G,连接DG.
平行四边形对角相等,有：∠ABC = ∠ADC = 60°；
所以,∠AGE = 90°- ∠ABC = 30°.
Rt△ABE中,∠AEB = 90°,∠ABE = 60°,BE = 2 ,
可得：AB = 4 ,AE = 2√3 .
Rt△ABG中,∠BAG = 90°,∠ABC = 60°,AB = 4 ,
可得：BG = 8 .
Rt△CFG中,∠CFG = 90°,∠CGF = 30°,CF = 1 ,
可得：CG = 2 .
所以,AD = BC = BG - CG = 6 ,EG = BG - BE = 6 ；
可得：AD = EG ,ADGE是平行四边形,对角线互相平分,有：AP = PG .
Rt△AEG中,∠AEG = 90°,∠AGE = 30°,AE = 2√3 ,
可得：AG = 4√3 .
直角三角形斜边上中线等于斜边的一半,
所以,PE = AP = PG = 2√3 .