I found this reference:

http://me.lsu.edu/~meniki/me3842/Notes/Drag&Lift.pdf
which states for a flat plate parallel to the flow under laminar flow conditions (not turbulent) skin drag coefficient is Cd=1.328/sqrt(Re_L), where Re_L is the Reynolds number based on the length of the plate:

Re_L = vL/nu, wher nu= the dynamic viscosity of the fluid.

Given this Cd the area to be used in the drag formula is the surface area of the plate, not its leading edge area. Hope this helps.