Trapezoidal modulation of quadrupole electrodes offers additional benefits to the concept of a radio-frequency quadrupole (RFQ). Because of the significant increase of the effective shunt impedance, RFQs with trapezoidal modulation have a reduced interelectrode voltage or resonator length as compared to conventional RFQs with sinusoidal modulation. This feature is especially valuable for RFQs operating in cw mode, since it reduces the required rf power. We develop a detailed procedure for the design of RFQ electrodes with trapezoidal modulation. With our design procedure and by properly choosing the trapezoidal cell parameters, we can easily control the peak surface fields in the RFQ to the same level as for sinusoidal cell modulation. The procedure is applied to the design of the electrodes for the ReA3 RFQ at Michigan State University.