Of course you can. you have all of the needed information. so first of all you should calculate distance from one point to another, let's say SouthWest and SouthEast. southWest coordinates (southLat,southLong) southEast coordinates (southLat, northLong), latitude stays unchanged.
Location l = new Location("southwest");
l.setLatitude(southLat);
l.setLongitude(southLong);
Location l2 = new Location("southeast");
l.setLatitude(southLat);
l.setLongitude(northLong);
double height = l.distanceTo(l2);
Same thing will go for the width of the rectangle, points will be SouthWest and NorthWest
southwest coordinates (southLat,southLong) northwest coordinates (northLat, southLong), longitude stays unchanged. we can use first location object "l" cause points are the same.
Location l3 = new Location("northwest");
l3.setLatitude(northLat);
l3.setLongitude(southLong);
double width = l.distanceTo(l3);
double area = width*height;
Sorry if there's some kind of syntax error, I was using the phone