Connect CE. Volume = bottom area * height.

Obviously, E-ABC is also a pyramid, because the area of ABC is equal to the area of DEF, so the height is equal. So the two pyramids, E-ABC and A-DEF, have the same volume.

Similarly, the two pyramids A-CDE and A-BCE have the same volume, because their base areas and heights are equal. A-BCE and E-ABC are the same pyramid, so the triangular prism is divided into three pyramids. A-DEF is one of them.

Therefore, the volume of A-FDE accounts for 1/3 of the volume of the whole triangular prism.