I assume you wanted to calculate an area of a portion of the sphere.
In that case you can split a spherical quadrangle into two spherical triangles, calculate the area of each and sum them up.
Check out some basic spherical trigonometry laws. That will tell you how calculate the diagonal of the quadrangle on a sphere.
Then, the area of each triangle can be found as:
area = (sum of angles) - Pi
Another approach would entail projecting the lat/lon coordinates into plane and calculate an area of the plane quadrangle. The projections usually cause area distortion unless you use equal-area projection.