Did I calculate correctly?

Hello! I have a question about the following invoice:

The total circumference of the sports area shown here should be 400m. Determine the radius r so that the rectangular area (between the two semicircles) is as large as possible.

Here is the sketch:

My approach:

HB: A= 2r • a (since 2r = d and d = b, I omitted b)

NB: 400 = 2πr (circumference) + 2a + 4r (rectangular circumference)

Then I transformed to a: -πr – 2r + 200= a

Then inserted into the HB: A= 2r ( -πr – 2r + 200) -> multiplied out A= -2πr^2 – 4r^2 + 400r

Then differentiate and set to 0, the result is r = 19.449.

Could someone please check if this is correct? 😅

Thank you