<span><span>АС1/С1В=1/1, ВА1/А1С=3/7, АВ1/В1С=1/3, S A1B1C1=S ABC - S AC1B1 - S C1BA1 - S A1CB1, обе части уравнения делим на S ABC</span></span>
<span><span />S </span><span>A1B1C1 / S ABC = 1 - (S AC1B1/S ABC) - (S C1BA1/ S ABC) - (S A1CB1/S ABC)</span>
<span /><span><span>S ABC=1/2*AB*AC*sinA, S AB1C1=1/2*AC1*AB1*sinA, AB=AC1+C1B=1+1=2, AC=AB1+B1C=1+3=4, </span>S AB1C1/S ABC=(AC1*AB1)/(AB*AC)=(1*1)/(2*4)=1/8,</span>
<span /><span>S </span><span>ABC=1/2*AB*BC*sinB, S C1BA1=1/2*C1B*BA1*sinB, BC=BA1+A1C=3+7=10, </span>
<span>S C1BA1/S ABC=(C1B*BA1)/(AB*BC)=(1*3)/(2*10)=3/20,</span>
S ABC=1/2*AC*BC*sinC, S A1CB1=1/2*A1C*B1C*sinC, S A1CB/S ABC=(A1C*B1C) / (AC*BC)=(7*3)/(4*10)=21/40,
S A1B1C1/S ABC=1-1/8-3/20-21/40=8/40=1/5, или S ABC/S A1B1C1=5/1