I guess it depends on how precise you want it.
If you want to be pretty accurate, I'd print it out as large as you can with relatively good detail. Then get thread and poster tack. place some poster tack at each major bend in the coast line, to hold the thread down, and run the thread around it, keeping it firm as you go.
When you finish. remove the thread and measure the length you used against the map's scale.
If you can be less precise, I'd load it up in to a program like photoshop and magic wand select the land mass.
Then, go to IMAGE --> Histogram - in the window, it will tell you how many pixels are selected.
Take the square root of that and you know how many pixels on a side that would be if it were a square you selected.
Then, measure in pixels the map scale (such as 10 pixels = 50 miles)
Multiply from there to get miles on each side of the hypothetical square.
And from there, go back to square miles.
And if you don't HAVE Photoshop, maybe you happen to know someone in real life who does and is good with it...
As for population, I'd just decide for each city how many people are in it. The
3E DMG has some rules of thumbs on city sizes. The area between the cities - just decide how many people per square mile and refer to your above calculation.
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