Answer
The total force required is proportional to the total cross-sectional area. Thus, the strain is proportional to the force per unit area.
Work Step by Step
If there were two wires, a force of $F$ would be required for each wire, thus, a total force of $2F$ would be required to produce the same strain $\frac{\Delta L}{L}$ in each wire. If there were $N$ wires, then a total force of $N\times F$ would be required.
$Force \propto (Strain \times N)$
$Force \propto (Strain \times Area)$
$Strain \propto \frac{Force}{Area}$
We can see that the total force required is proportional to the total cross-sectional area. Thus, the strain is proportional to the force per unit area.
