c^2=a^2-b^2=2-1=1,c=1,左焦点坐标为（-1,0）,直线AB斜率为tan(π/4)=1,由点斜式,得直线AB方程为y=x+1,即x=y-1,将其代入椭圆x^2/2+y^2=1,得3y^2-2y-1=0,y=1或-1/3（A,B纵坐标）△F2AB的面积为(1/2)*|F1F2|*|1-(-1/3)...