Using the properties of cross sections and middle cross sections of a parallelogram

Using the properties of cross sections and middle cross sections of a parallelogram,
P = middle of BD
h = height of pyramid

DKBL = DNBM
V_KBLMDN
= V_KBLMPN + V_NPMD
=S_KBL(h/2) + (1/3)S_PNM*(h/2)
=(h/2)S_KBL(4/3)
=(h/2)(1/4)S_ABC(4/3)
=(1/2)hS_ABC(1/3)
=(1/2)V_pyramid