(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I want to find the area of a quadrilateral whose four vertices are the four points on the earth.Suppose,they are the four cities in a country.They enclose a "quadrilateral" in the sense that the curvature of the earth is assumed to be neglected across that area.We know the latitude and longitude of each of those points.

2. Relevant equations

3. The attempt at a solution

If we knew the Cartesian co-ordinates,it would not be a problem...We could first find the lengths of the sides and hence,the area of the two back to back triangles separately and then,could add them up.But, here all we are given is the angular co-ordinates.

I wonder if the following process will do.First we will use the relation S=R (theta) to find the arc length along the constant latitude line...between two points.Then,the arc length along the constant longitude line.Suppose they are x and y.Then, the length of the side of the quadrilateral is [tex]\sqrt {x^2+y^2}[/tex]...And then,we can use the same process as earlier to find the area of the quadrilateral.

What is also thrilling me is that how to do the same if the curvature of the earth is not neglected...

The expression should be [tex]\int [sin\theta d\theta d\phi ] [/tex]

I am thinking more...and hopefully,I will be able to give some more details...

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# Homework Help: Finding the area of a big quadrilateral on the earth

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