如图,四边形ABCD中,∠BAD=∠C=90°,AB=AD,AE⊥BC于E,若线段AE=5,则S四边形ABCD=_.
问题描述:
如图,四边形ABCD中,∠BAD=∠C=90°,AB=AD,AE⊥BC于E,若线段AE=5,则S四边形ABCD=______.
答
过A点作AF⊥CD交CD的延长线于F点,如图,∵AE⊥BC,AF⊥CF,∴∠AEC=∠CFA=90°,而∠C=90°,∴四边形AECF为矩形,∴∠2+∠3=90°,又∵∠BAD=90°,∴∠1=∠2,在△ABE和△ADF中∠1=∠2∠AEB=∠AFDAB=AD∴△ABE...