Let l represent the length of fence parallel to the side of the building. Then the width will be that of half the remaining fence, (800 -l)/2. The total area will be
A = lw = l(800 -l)/2
This is the equation of a downward-opening parabola with zeros at l=0 and l=800. The zeros are symmetrical about the axis of symmetry of the parabola, which axis goes through the vertex. That is, the vertex is located at
l = (0 +800)/2 = 400
The maximum aea that can be enclosed is 400 m long by 200 m wide, so is
(400 m)×(200 m) = 80,000 m²
