We label the points on the window for convenience:

Perimeter p, where p = f(r):

p = circumference of the semicircle + length AB + length BC + length CD

p = (2π r) + (2r + 10) + 2r + (2r + 10)

p = π r + 6r + 20

Since the radius cannot be negative, and there would be no window if r = 0, then...

The domain of the function is: all real values, 0 < r ≤ R, where R is some maximum possible value of r (determined by design considerations).