Answer
$.333mgh$
Work Step by Step
We know that the center of mass of a uniform isosceles triangle on its base is 1/3 of the way to the top, or $.3333h$. We know that when it is flipped onto its apex, its center of mass will be $1h-.3333h=.66667h$. Thus, we find that the energy needed is:
$\Delta U = mg(.667-.333)h=.333mgh$
