A screen shot, top view.
Left = unselected polygon curve converted to mesh and ready to extrude.
Right = unselected polygon curve in edit mode. It was constructed by adding pink dots with mouse clicks, then snapping the dots and lines to the grid to form sharp corners.
Shaded working model of the extruded arena showing the outline of the original curve in dark gray at the right:
Opposite side, that is outside the arena from above, toward the back and right:
back to the map