ffutures | Maths check again?

Here's a passage from Weinbaum's "The Mad Moon" describing Io

"The whole little planet was mad—loonies, parcats, slinkers and Grant Calthorpe—all crazy. At least, anybody who ever ventured outside either of the two polar cities, Junopolis on the north and Herapolis on the south, was crazy. One could live there in safety from white fever, but anywhere below the twentieth parallel it was worse than the Cambodian jungles on Earth."

Now, if I'm reading this right it means that the danger zone extends to 20 degrees either side of the equator, and the rest of the moon is OK. Which means that they aren't actually short of space.

The trouble is that my geometry is so rusty that I can't remember how to work out what proportion of the surface is inside and outside these zones. I've worked out that since Io is 3660 Km in diameter, about half the size of Mars, the surface area of the whole moon is a little over 42 million square kilometers - about 42,083,519 to be precise. Anyone able to do the rest of the calculation?

Later I've got three different answers, all of which say that the safe zones are each bigger than the USA!

And I've just realised that this description doesn't work at all with a tidally locked world, despite Weinbaum actually giving the length of day as the same as the orbital period. Something really does not compute...

Later still Unless it rotates in the opposite direction to its orbit, of course.