The bottom of p-abcd is a parallelogram, the bottom of PA ⊥ is ABCD, e is a point on PA, and the section of PC ∥ is BDE Find the volume ratio of the two parts of the pyramid p-abcd divided by the section BDE

The bottom of p-abcd is a parallelogram, the bottom of PA ⊥ is ABCD, e is a point on PA, and the section of PC ∥ is BDE Find the volume ratio of the two parts of the pyramid p-abcd divided by the section BDE

Let the bottom area be s and the height be H
Connect AC and BD, set AC to BD in O, and connect EO
PC parallel plane EBD
PC included in PAC
The intersection of EBD and PAC is EO
So PC parallel OE
So e is the midpoint of PA
Ve-abd=(1/3)*Sabd*EA=(1/4)*(sh/3)=(1/4)Vp-abcd
The volume ratio of the two parts is 1:3