I don't have it in front of me, but I do remember the map is missing its scale. For a quickie measure, check the size of the central natatorium on its detail map, and use that as a scale on the larger island map.
Took a look this morning. Using the natatorium as a scale, we can assume the island is just shy of 2,000-feet long, so under a half-mile. Obviously a wee bit less wide than that. Hope that helps!