One troubling thing is that I looked on the internet and got three different values for the area of the state. I would think in the age of GPS we would have that figured out to a pretty precise amount. The three amounts were separated by 94 square miles. At least that gives me some wiggle room.
I figured I could find both the length and width of the state would be with:
(arc length)/360(2pi(radius of the earth))
The radius of the earth is 3,959 miles. The arc length I figured would be the differences in the latitudes or the longitudes. The height came out great. I got 276.4, and the web says 276. The width wasn't even close: my 483.7 to their 387. Mine was too big. Arc length would include the curvature of the earth. I thought maybe I could use Law of Cosines to get a closer figure.
C^2 = (3959)^2+(3959)^2-2(3959)(3959)Cos(7)
It was interesting that I got 483.4 as compared to an arclength of 483.7. What was not interesting was the web says the length of Colorado is 387.
What I learned:
1. I noticed their published lengths and widths didn't multiply to get their published area. It was 104,091 to 106,812 square miles. So, they must not use length x width to get the area. That makes sense, because that would only work on rectangular states of which there are not many.
2. Why my method didn't work. I knew this but didn't think about it - lines of longitude are not the same distance apart. They are a certain distance apart at the equator and shrink to nothing at the poles. I guess that is why my north-south distance came out accurately but my east-west was way off.
So, I don't know how they find the area of a state or any region for that matter.
There's a good project for you or your students.
