I was curious as to how the land area of a state such as Colorado could be calculated. I understand the area of a 2D rectangle can be calculated using the formula width times length. However, I was wondering how being on a curved surface affects this area.
For example, Wikipedia states the length, width, and area of Colorado to be 610km, 450km, and 269,837 square kilometers. Assuming Colorado is perfectly rectangular, the area by multiplying the length and width is 274,500 square kilometers, which is greater than the quoted area.
So, I have a few questions:
- How would one theoretically calculate the area between four points on a sphere, and could this be applied to an ellipsoidal shape?
- Apologies if this does not fit on the Math stackexchange, but how is land area calculated in the real world?