#Pyth, 34 bytes

    KCcQ2c.asm*@hKd-@.<eK1d@.>eK1dU3 2

[Try it online.][1]

Works by calculating abs(a*(d-f) + c*(f-b) + e*(b-d))/2 from input a,b,c,d,e,f.


  [1]: http://pyth.herokuapp.com/?code=KCcQ2c.asm%2a%40hKd-%40.%3CeK1d%40.%3EeK1dU3+2&input=1%2C2%2C4%2C2%2C3%2C7&debug=0