已知,在四边形ABCD中,角BAD=角c=90度,且AB=AD,AE垂直BC垂足为E,若AE=2倍根号3,求四边形的面积_数学解答

已知,在四边形ABCD中,角BAD=角c=90度,且AB=AD,AE垂直BC垂足为E,若AE=2倍根号3,求四边形的面积

人气：420 ℃　时间：2019-08-20 04:51:57

解答

过点D,作D⊥AE与E
则ΔDFA≌ΔAEB
BE=AF,DF=AE
SABCD=SΔDFA+SΔAEB+SDFCE
=1/2DF*AF+1/2BE*AE+DF*EF
=1/2AE*AF+1/2AF*AE+DF*EF
=AE*AF+DF*EF
=AE*(AE-EF)+AE*EF
=AE^2
=12