If the diameter of the area of is not more than a few kilometers (or miles if you insist) then
1) transform the coordinates to x,y space with unit meters
2) Use the simple formula areaint
for 1): convert lat and long which are in unit degrees to meters, by multiplying with a factor
f = 40 000 000 / 360. // or use a more exact value using the WGS84 equitorial radius
(Circum fence of earth in meters divied by 360 degrees)
so
x = longitude * f;
y = latitdue * f
addionally multiply x with the cos(averageLatitude), this eliminates the fact that lat and lon have not the same scale (on equator the distance between two degrees of longitude is aproxx 111km, while on the north pole it is 0.
x= x * cos(toRadians(averageLatitude));
The result is the area in square meters.
The averageLatitude is the mean value of all latitude coordinates of that area
solved Multiple Lat/Long Coordinates to Miles [closed]