What does “cross section area” mean when dealing with stress/strain?

1. The problem statement, all variables and given/known data

For clarification, here is an example problem:

A circular steel wire 2 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire?

Relevant equations

FL = YA(ΔL)

Apparently, the cross section area for this object is simply pi*r^2 (as for any circle). Can someone tell me exactly what the cross section area is supposed to refer to? I thought it was the area of the plane of the object perpendicular to the applied force, but apparently I’m wrong or not understanding something properly.

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