review paper
Traditional method: comparison of the processes
e+e- -> J/ψ -> l+l-
and
e+e- -> J/ψ -> hadrons
since their cross sections are proportional to Γ(e+e-)Γ(l+l-)/Γ(tot) and Γ(e+e-)Γ(hadrons)/Γ(tot) respectively.
Assuming lepton universality, Γ(e+e-)=Γ(μ+μ-)=Γ(l+l-).
Another assumption is that there are no other possible decays, so that:
Γ(tot)=2*Γ(l+l-)+Γ(hadrons).

The branching ratios for lepton pairs, BR(l+l-)=Γ(l+l-)/Γ(tot), where extracted together with Γ(tot).
So, we have three observables (BR(l+l-), σ(l+l-), σ(hadrons)), and we want to extract Γ(tot).
Knowing BR(l+l-) and σ(l+l-), we extract Γ(e+e-).
Knowing Γ(e+e-) and knowing how to relate Γ(hadrons) to it and to Γ(tot), now σ(hadrons) has only a dependence on Γ(tot).

The area under the peak is given by 6π²BR(J/ψ -> e+e-)*BR(J/ψ -> hadrons)*Γ/M².