Yeah, does this refer to the square footage, or like the area surrounding the house?
Yes, I believe that it does. I looked it up and Leo confirms. EDIT: I see that someone is sad about my comment and downvoted it. I see now that my comment was unclear, so I will try again. In Leo it shows "Fläche" as meaning BOTH "square footage" AND an area (region, district, etc.). therefore, it appears that this could mean either the dimensions of the house or the area where it is located. Would love to get a native speaker's opinion on this one.
I've looked on Google Translator's examples of the use of the word "Fläche", and I think that is most used on the sense of measurement, with "area", "surface" and "face/side" as the most frequent translations. Give it a try, on the baloon button:
The translation says it's the area of the house (singular), so why is it Hauses instead of Haus?
One of the definitions is "side", but "the side of the house" is incorrect?
First of all, it's not a complete sentence, and secondly, sentences as a whole don't have cases -- parts of sentences have cases.
die Fläche des Hauses is a noun phrase. As a whole, it's in the nominative (or perhaps accusative) case.
The part des Hauses is in the genitive case.
Only masculine singular nouns have an accusative form that's different from the nominative.
So die Fläche can be nominative or accusative -- and since this is not a whole sentence but just a phrase standing alone, you can't tell how it might have been used in a sentence.
For example, if someone asks, Was berechnest du? -- Die Fläche des Hauses. (What are you calculating? -- The area of the house.) it would be accusative, the object of berechnen "to calculate". (Short for Ich berechne die Fläche des Hauses.)
But if someone asks, Was ist diese Zahl da? -- Die Fläche des Hauses. (What is that number there? -- The area of the house.) it would be nominative -- the full form would be Diese Zahl ist die Fläche des Hauses, with die Fläche des Hauses being the predicate nominative after ist.
it´s sound the same "ä " and "e" or is there any difference that i do not hear it?
It's hard when your first encounter with such a word is the spoken exercise. I got the written version first--this time. Just take the time to see how it is spelled so it doesn't fool you again!
As a native German speaker I have a question to the native English speakers: Isn't there a different word for "Fläche" than "area" in English? For my understanding "an area" is a more large area [Gebiet], not closer specified and a "square footage" ist too specific [Quadratmeterzahl]. I understand "Die Fäche des Hauses" as the occupied area of a house itself and not the property [Das Grundstück] it stands on?
"Area" can mean either a region or a measurement of how much two-dimensional space it takes up (e.g., in square feet). "Area" is the word to use to talk about that measurement (so it works fine for "Fläche").
Usually we say "the area around something" to talk about the region it's in ("The area around the house is full of weeds") and "the area of something" to talk about its 2D measurement ("The area of the house is 1000 square feet"). So I read "the area of the house" as talking about the measurement rather than the region around it.
It would not accept "side" for me. In Math class we always talked about the sides of a shape as Flaeche (sorry, don't know the keyboard commands from my laptop without the special buttons). This is the first as I've heard about it in this way, but I've always only heard it in the mathematical (mainly Geometry) sense.
In Math class we always talked about the sides of a shape as Flaeche
Fläche would be fine for the size of a three-dimensional shape such as a cube, but for a two-dimensional shape such as a hexagon, I would understand Fläche only as the area inside the shape, not as one of the sides.
But here, the context is a house, not a mathematical shape.