Hi there! Hopefully this helps!
We know pi*r^2 gives the area of the circle. And the diameter is 2*r.
Now the area of the circle is 201.1 in^2.
Therefore 201.1 = pi*r^2
=> r^2 = 201.1 / pi
=> r^2 = 64.0 (approximately)
=> r = sqrt 64
=> r = 8
Diameter = 2*r = 2*8 = 16