Answer
400 by 800 rectangle
Work Step by Step
We know that the memorial must be at least 200 feet away from the boundary of the park. Thus, we find the dimensions of the park:
$$ 1200-(2)200=800 \\ AND \\ 800-(2)(200) =400$$
The locus of points is a 400 by 800 rectangle in the center of the rectangular park.
