AB=3FB BC=3DC CA=3EA DEF的面积是4 ABC的面积是( )

令FB=x,EA=y,DC=z,则
S=Sa+Sb+Sc+So
S=(1/2)*3x*3y*sinA=(1/2)*3x*3Z*sinB=(1/2)*3y*3z*sinC
即s=(9/2)xysinA=(9/2)xzsinB=(9/2)yzsinC
Sa=(1/2)*2x*y*sinA=xysinA
Sb=(1/2)*x*2z*sinB=xzsinB
Sc=(1/2)*2y*z*sinC=yzsinC
So=4,
3S=3(Sa+Sb+Sc+So)
(9/2)(xysinA+xzsinB+yzsinC)=3(xysinA+xzsinB+yzsinC+4)
xysinA+xzsinB+yzsinC=8
故S=8+4=12.