easy answer -
the whole plane is part of the lift
lift is nothing but drag put to work for you.
when the drag no longer works against gravity -it ain't lift.

You can make fancy computations and theorize till the cows come home - but it still remains a fact - all of the plane is at somtimes or another - part of lift.
maybe lousy lift -but still lift.
Take a pair of scissors and cutout a shadow of the entire airframe - figure that area - - all of that, can be lift.
from old habits - and ease of comparison- many folks just use projected wing area -but that is not a true representation of all the lifting parts..
The formula for this is probably in some book -