Does this relate to Heron?

Algebra Level 1

\[ \begin{eqnarray} a + b + c + d &=& 12 \\ a + b + c - d &=& 10 \\ a + b - c + d &=& -2 \\ a- b + c + d &=& 6 \\ -a + b + c + d &=& 10 \\ \end{eqnarray} \]

\(a,b,c,d\) are positive integers satisfying the equation above.

What is the value of \(a \times b \times c \times d \)?

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