∵双曲线y=kx(x＞0)，经过矩形OABC的边AB，BC中点F、E，且四边形OEBF的面积为2，∴S△OBF=S△OAF=12S△OBC=14S矩形OABC，S△OCE=S△OBE=12S△OAB=14S矩形OABC，∴S△OAF=S△OEC=14S矩形OABC=12S四边形OEBF=12|k|=1．...