This research focuses on the exponential stability of the nonlinear Saint-Venant equations within a trapezoidal channel. We examine a general framework that incorporates arbitrary friction, spatially varying slopes, and channel geometry variations, resulting in non-uniform steady states. To analyze stability, we construct an explicit quadratic Lyapunov function as a weighting function for small perturbations around the steady state. It is then demonstrated that, with a well-designed boundary feedback control, the nonlinear Saint-Venant equations governing a trapezoidal channel achieve local exponential stability in the \( H^2 \) -norm. Finally, we explicitly define this control and validate our findings through numerical simulations.