cos∠BAD=(2²+1²-BD²)/(2*2*1)=(5-BD²)/4
cos∠DAC=(1²+1²-DC²)/(2*1*1)=(2-DC²)/2
因∠BAD=∠DAC,
所以(5-BD²)/4=(2-DC²)/2,BD²-2DC²=1
又AB/AC=BD/DC,2/1=BD/DC,BD=2DC
(2DC)²-2DC²=1,DC=√2/2,BD=2*√2/2=√2,BC=√2/2+√2=3√2/2≈2.12.
(2+1+2.12)/2=2.56
S△ABC=√[2.56*(2.56-2)(2.56-1)(2.56-2.1)]≈1.01