How do you solve this equation without positively knowing the shape of both the walkway and the pool? i am very specific and indecisive so simple/vague things confuse me and this seems like one of those times. i'd know how to solve the problem if i knew the shapes.

See my diagram

I'm assuming that your swimming pool is an oval or something like that
remember that the area of an oval is r₁r₂π where r₁ and r₂ are the 2 radii

so

we must do big oval-small oval

the radius is half of the diameter

calculating smalller oval area
it is 32 by 18
those are diameter
halve them
16 by 9
so the area is 16*9*pi or 144pi square feet

big oval area
add 3 feet to each side, so 6 feet total to each dimention
the big oval has diameters of 32+6 and 18+6 or 38 and 24
halve them to find the radii
19 and 12
the area is 19*12*pi or 228pi

so the area that is concrete=228pi-144pi=84pi squaer feet or about 263.89 square feet

Yes, two vertical lines can be complementary