We want to cut a small pyramid which weights half of the original pyramid's weight.


For it, the volume of the small pyramid must be half of the volume of the original pyramid.


The small pyramid and the original pyramid are geometrically similar with the similarity coefficient c = ,

where h and H are altitudes of the small and the original pyramids, respectively.


So we want   =  =  = 0.5.


It implies  h =  =  = 0.952441 meter.



ANSWER.  The cutting distance from the vertex should be  0.952441 of a meter.