设扇形的圆心角为A,扇形的半径为R.
则：S=PI*R^2*A/(2*PI)=A*R^2/2=2
周长=2*PI*R*A/(2*PI)+2*R=R*A+2*R=6
A*R^2/2=2
A*R+2*R=6
R*(A+2)=6
R=6/(A+2)
A*R^2/2=A*(6/(A+2))^2/2=2
18*A=2*(A+2)^2=2*(A^2+4*A+4)
9*A=A^2+4*A+4
A^2-5*A+4=0
(A-4)(A-1)=0
A=1弧度或A=4弧度
R=6/(A+2)=2cm或R=6/(A+2)=1cm