Vì A1,B1,C1,D1A1,B1,C1,D1 là trung điểm của BC,CD,DA,AB
⇒SADD1=12SADB,SBB1C=12SBDC⇒SADD1=12SADB,SBB1C=12SBDC
⇒SADD1+SBB1C=12SABCD⇒SADD1+SBB1C=12SABCD
Tương tự: SABA1+SCC1D=12SABCDSABA1+SCC1D=12SABCD
⇒SABCD=SADD1+SBB1C+SABA1+SCC1D⇒SABCD=SADD1+SBB1C+SABA1+SCC1D
Mà: SABCD=SAMD1+SAMQC1+SC1QD+SDQPB1+SCPB1+SPCA1N+SBNA1+SBNMD1+SMNPQSABCD=SAMD1+SAMQC1+SC1QD+SDQPB1+SCPB1+SPCA1N+SBNA1+SBNMD1+SMNPQSADD1+SBB1C+SABA1+SCC1D=SAD1M+SAMQC1+SDQC1+SDQC1+SDQPB1+SB1CP+SB1CP+SCPNA1+SBNA1+SBNA1+SBD1MN+SAD1MSADD1+SBB1C+SABA1+SCC1D=SAD1M+SAMQC1+SDQC1+SDQC1+SDQPB1+SB1CP+SB1CP+SCPNA1+SBNA1+SBNA1+SBD1MN+SAD1M
⇒SMNPQ=SAMD1+SBNA1+SCPB1+SDQC1(đpcm)