Does this relate to Heron?

Algebra Level 1

a+b+c+d=12a+b+cd=10a+bc+d=2ab+c+d=6a+b+c+d=10 \begin{aligned} a + b + c + d &=& 12 \\ a + b + c - d &=& 10 \\ a + b - c + d &=& -2 \\ a- b + c + d &=& 6 \\ -a + b + c + d &=& 10 \\ \end{aligned}

a,b,c,da,b,c,d are positive integers satisfying the equation above.

What is the value of a×b×c×da \times b \times c \times d ?

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