Theoretical because they haven’t tested it yet that is just their hypothesis
Check the picture below.
a)
so the perimeter will include "part" of the circumference of the green circle, and it will include "part" of the red encircled section, plus the endpoints where the pathway ends.
the endpoints, are just 2 meters long, as you can see 2+15+2 is 19, or the radius of the "outer radius".
let's find the circumference of the green circle, and then subtract the arc of that sector that's not part of the perimeter.
and then let's get the circumference of the red encircled section, and also subtract the arc of that sector, and then we add the endpoints and that's the perimeter.


b)
we do about the same here as well, we get the full area of the red encircled area, and then subtract the sector with 135°, and then subtract the sector of the green circle that is 360° - 135°, or 225°, the part that wasn't included in the previous subtraction.

Independent variable (im pretty sure sorry if im wrong)
In order to solve this, we need to select the function that meets our constraints. Since x^2 - 5 occurs when x is less than 3, and the x-value we are given is -4, we use the first function.
f(-4) = (-4)^2 - 5
f(-4) = 16 - 5
f(-4) = 11