Are you using JK2Radiant or GTKRadiant? Use the clipper tool to split the cone in half. Hold down Ctrl and right-click to place the first clipper dot and do the same for the second one. Move them around until you have the yellow line cutting through the middle of the cone and so that the good side is on one half and bad side is on the other. Then hit enter+shift to split it and then just delete the bad half.
Don't you hate pants?