Active matrix backplanes including an array of hexagonal electrodes or an array of triangular electrodes. Because the backplane designs route the gate lines along the periphery of the electrodes there is less cross talk with the surface of the electrode. The disclosed designs simplify construction and control of the electrodes and improve the regularity of the electric field above the electrode. Such backplane electrode designs may be particularly useful in electrowetting on dielectric (EWoD) devices and electrophoretic displays (EPD).