Given the area of a circle = 201.1 in^2.

We need to find the length of the diameter of the circle.

We will use the area of a circle formula to find the radius.

We know that:

The area of the circle = r^2 * pi where r is the radius.

Let us substitute.

==> A = r^2 *pi

==> 201.1 = r^2 *pi

Now we will divide by pi.

==> r^2 = 201.1/ pi = 64.01

==> r= 8 ( approx.)

Then the radius of the circle is 8 in.

But we know that the diameter is twice the radius.

==> The diameter = 2* r = 2*8 = 16

Then, the length of the diameter = 16 in.

We know the area of the circle is given by pi*r^2. 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

**Therefore the required diameter is 16 in.**

Let the diameter of the circle be 2r and radius r.

Then the area of the circle = pir^2 .

The actual area of the circle = 201.1 in^2.

Therefore pir^2 = 201.1.

Therefore r^2 = 201.1/pi/

=> r = sqrt(201.1/pi).

So the diameter of the circle = 2r = 2sqrt(201.1/pi) = 16.00 inch nearly.