How is the terrace area calculated?

Calculated according to which method? Old calculation from the year of construction of the object DIN 283. Or DIN 277. Or Residential Space Ordinance. Or 2.BV. Alone the difference according to the current methods DIN 277 and Residential Space Ordinance can be up to 40%. So don't obsess over one number. Just stating living space xy sqm doesn't say anything at all.

And balcony and non-terrace areas must not be counted at full square meters according to DIN 9472 from 1877 either

If you add up the rooms, 10 sqm are already missing. And balcony and non-terrace areas must not be counted at full square meters according to DIN 9472 from 1877 either

But with DIN 277 always 100%. Other areas, which are not living spaces according to the Wohnflächenverordnung, are also creditable there.

Just upload all documents here.

No! It is NOT A TERRACE AT ALL!