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I'm studying English with Murphy's Grammar in use and I'm puzzled with something. I have this exercise where I have to put in the right preposition. But it's not the problem. 
All objects on these pictures are being described with the "the" article except the last one - "a farm" (it's not my opinion, it's in the answers). Why so? Is it because we can't see the farm itself, but only piles of straw? But we also can't see the whole sales department, we see only one desk. Please, help me out.
Just like the book, for most of these, I would use the indefinite article, too. One exception might be sales department. Mind you, it seems that a sales department would be just as valid as the sales department – except for one subtle clue: they have named the sales clerk. (Now that we know it's the sales department where Sue works, the indefinite article is no longer preferred.)
That said, I'd be encouraged by your bewilderment. I think the book would have been better off leaving Sue out of it, and using a sales department instead. I think they've worked too hard to set up a picture where the reader toward be steered toward the instead of a; that is, I think they have overreached. Had they given the farmer a name, I suspect they would have again used the farm instead of a farm.
Another place where I would agree with you is #3. In #4, I would probably use the corner, because we often say, "Go stand in the corner" (even when a room has more than one corner). However, in #3, the corner is generic. If Linda knew where she was, I'd probably say:
Linda is standing on the corner [of Elm Street and 5th Avenue].
However, if Linda was unfamiliar with the city, I might say:
Linda is standing on a corner [wondering where she is].
Also, #6 is interesting. Again, it depends on the context. If it was my car, I would describe that as the back of the car:
Put the groceries in the back of the car.
However, if it was just some random automobile, I might describe it as the back of a car.
I saw a blue car with a dent in the back.
Actually, with most of the examples, only the definite article would be used, since, together with the correct preposition they define a specific position.
For example, the post office is on the left. If you would say it is "on a left", it would not only sound strange, it would imply that the post office is somewhere on a street to my left. ("A left" meaning a left turn, not "the left side of something"!)
You could say you are on "a second floor" somewhere, but this usage is very rare. Regardless of which specific building you are in, you will normally say you are on the nth floor.
Likewise, a flight of stairs only has one top, so you are at the top of the stairs. (Not "a" stairs, since stairs are plural anyway.)
With farm, you would use "the" to indicate a specific farm, but if you want to say it could be any farm, you use the indefinite article.
The only other places where you could use "a" would be the two corners. Being on the corner or being on a corner can both be used, but usually you would say "I am on the corner of a street."
In a corner and in the corner have different meanings. If you are in the corner, you are literally in the corner-area of a room. If you are in a corner, this will be understood figuratively, as being in a difficult position.
A long story short: most of these expressions are idiomatic and always used with the definite article. The one real exception is indeed the farm, where neither "a farm" or "the farm" have any idiomatic meaning.
It is a bit confusing that in the answers they chose to use the indefinite article, when the definite article could be used as well.
(Maybe they originally tried to go fro "in the country", which has an idiomatic meaning of "in a rural area", as opposed to "in a country", which means "inside the borders of a state")
