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Here we demonstrate significant improvements in the performance of supercapacitor electrodes based on 2D MnO2 nanoplatelets by the addition of carbon nanotubes. Electrodes based on MnO2 nanoplatelets do not display high areal capacitance because the electrical properties of such films are poor, limiting the transport of charge between redox sites and the external circuit. In addition, the mechanical strength is low, limiting the achievable electrode thickness, even in the presence of binders. By adding carbon nanotubes to the MnO2-based electrodes, we have increased the conductivity by up to 8 orders of magnitude, in line with percolation theory. The nanotube network facilitates charge transport, resulting in large increases in capacitance, especially at high rates, around 1 V/s. The increase in MnO2 specific capacitance scaled with nanotube content in a manner fully consistent with percolation theory. Importantly, the mechanical robustness was significantly enhanced, allowing the fabrication of electrodes that were 10 times thicker than could be achieved in MnO2-only films. This resulted in composite films with areal capacitances up to 40 times higher than could be achieved with MnO2-only electrodes.