Pyth, 34 30 bytes
KCcQ2c.asm*@hKd-@eKhd@eKtdU3 2
Works by calculating abs(a*(d-f) + c*(f-b) + e*(b-d))/2 from input a,b,c,d,e,f.
Pyth,
Sam Cappleman-Lynes
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