Answer:

To find the value of \(xy + yz + zx\), we can use the following formula:

\[xy + yz + zx = \frac{1}{2} \left((X + Y + Z)^2 - (X^2 + Y^2 + Z^2)\right)\]

Substitute the given values:

\[xy + yz + zx = \frac{1}{2} \left((12)^2 - 64\right)\]

\[xy + yz + zx = \frac{1}{2} \left(144 - 64\right)\]

\[xy + yz + zx = \frac{1}{2} \times 80\]

\[xy + yz + zx = 40\]

So, the value of \(xy + yz + zx\) is 40.