Path A,B-S,T Net Area
Since thickness is not constant along the path, it is easier to look at this problem in different manner than you would if you had a constant thickness along the path.
The logical approach is to look at things in terms of AREA. In this approach you add and subtract area from the member gross area.
Net Area = Gross area - Cross Sectional Area of Holes + Additional Area Due to Stagger
For this problem, all the holes are on the web. The area reduction for a hole on the web equals the effective diameter of the hole times the thickness of the web.
EFFECTIVE HOLE DIAMETER = bolt dia. + 1/16" for std hole + 1/16" damage allowance
HOLE AREA = (effective hole diameter) * t
All the holes are in the flanges so:
FLANGE WEB HOLE AREA = (.875" + .125") * (0.720") = 0.720 in2
There are no staggers on this path so:
Net Area = Ag - 4 hole areas
Net Area = 20.0 in2 - 4*(0.720 in2) = 17.12 in2