m与n垂直,故：m·n=0,即：(sinA,sinB-sinC)·(sinC-sinA,sinB+sinC)
=sinAsinC-sinA^2+sinB^2-sinC^2=0,即：ac+b^2=a^2+c^2,由余弦定理：
cosB=(a^2+c^2-b^2)/(2ac)=1/2,故：B=π/3
外接圆的面积：S=πr^2=4π,故：r=2,而：b/sinB=2r,故：b=4sinB=2sqrt(3)
b=ccosA,即：cosA=(b^2+c^2-a^2)/(2bc)=b/c,即：a^2+b^2=c^2,故△ABC为直角△
故：a=b/tanB=2,故△ABC的面积：S1=ab/2=2sqrt(3)你那个2sqrt(3)是什么sqrt(3)就是根下3，二次根下的意思，sqrt(3)=1.732