For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented. For wave equations with variable coefficients on regions which are not necessarily smooth, we obtain a sufficient condition for the subregion on which the application of control will yield the exact controllability property by using piecewise multiplier method and Riemannian geometry method. Some examples are presented.