Chess:
It seems to me that the Wolfram language (including standard packages) continues to grow at fast pace that makes it challenging for the tech writers to keep up with the documentation.
I have found a several functions like that have features like Area that are not explicitly documented.
In the case of "Listable" functions, there is more than one way to make a function "Listable". If you have a function that takes a single argument, then to make it Listable is to add the Listable attribute. But, for functions that take more than one argument, I think you need to do a bit more work and provide an explicit definition for what to do when you get a list.
In the case of Area, I first assumed that there must be two single argument definitions. For example, I can create a function that takes either either a scalar or a list (without using the Listable attribute) using something like:
Clear[f];
f[x_?NumericQ, multiplier_?NumericQ] := x * 2;
f[l_List, multiplier_?NumericQ] := Map[f[#, multiplier] & , l];
But, if this were the case with Area, then:
Area[{Disk[{0, 0}, r], Sphere[{0, 0, 0}, r]}]
would give the same answer as:
{Area[Disk[{0, 0}, r]], Area[Sphere[{0, 0, 0}, r]]}
But that's not the case here. Passing the list into Area gives a pair of constrained equations:
{ConditionalExpression[\[Pi] r^2, r > 0],
ConditionalExpression[4 \[Pi] r^2, r > 0]}
But since calling Area with just a single geometry yields simple expressions (even if Mapping a list on to Area):
{\[Pi] r^2, 4 \[Pi] r^2}
So, now I am not so sure what is going on with Area. But I think that it is likely that we will all continue to run into surprises like this for some time.
Thank you for the great question. Trying to answer questions like this helps me to better use the language, even when it leaves me a bit confused.
