Re: When land area measurements are given, do they include topography?

Thank you very much for your question anonymous and i hope i'll provide 
you with a satisfactory simply given answer.

It is true that when you have a two dimensional (2D) shape, for example a 
circle, than the area calculated from the same shape after adding a new 
dimension (height), for example a hemispherical shape, will be different.
(For those interested A(circle)=pi*R^2 and A(hemispere)=2*pi*R^2)

Now when we go to real life, let's say you own a lot somewhere and you ask 
from a surveyor engineer (or land engineer depending on which country you 
live) to measure the lot and tell you how big it is, that is its area. The 
surveyor will provide you with the area of the lot without taking into 
account the height differences but only the projection of the lot's edges 
on a flat surface (that is the map surface). In simple words imagine that 
you are on a plane and you project all the points which have a height 
difference onto the plane you stand. Then you calculate the area on the 
plane.
To conclude the example the surveyor would also provide you with heights 
for your lot, usually in case you want to calculate slopes and volumes.

So for the example you mentioned the area is not affected whether you are 
in the Rocky mountains or in Florida. The way you measure the area is the 
same as the one described above. But remember that heights are always 
provided.

Ofcourse there are also other things that are taken into account like the 
earth's curvature, especially when high accuracy is needed, but this is a 
more complicated matter. 

If you or anyone is interested in this topic than any handbook of 
surveying engineering could provide additional information.

MSc. Eng. Vassilios N. Grigoriadis
Dept of Geodesy and Surveying
Aristotle University of Thessaloniki
Makedonia, Greece