∵2asinB-根号3b=0
∴2sinAsinB-√3sinB=0
∵sinB≠0
∴2sinA-√3=0
∴sinA=√3/2
∵锐角三角形
∴A=π/3
(2a^2=b^2+c^2-2bc•cosA
36=b^2+c^2-bc
=（b+c）^2-3bc
=64-3bc,
∴bc=28/3,
又sinA=√3/2,
则S△ABC=1/2bcsinA=7√3/3