However, TAI did update their website for Hurjet when they ended up choosing GE F404 instead of Eurojet EJ200. So I thought they would do the same with any change.
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Anyhow, I have figured out the inconsistency in Wing Area between the TAI's official information for Hurjet on their website and on their official broucher. It seems like some dumb employee fails to correctly convert the numbers in the imperial system into the metric system. Wing Area of Hurjet is 270 ft2 and the figure consists with the figure both on the broucher and on the website.
270 ft^2 is about 25 m^2, so the broucher is correct. This mistake is understandable since Turkish engineers who probably learnt from American as they are a user of American fighter jets would probably also use the imperial system for designing aeroplanes.
Now, It doesn't mean Hurjet theoretically won't be able to carry 5000kg of payload since Super Skyhawk which had the same engine and a smaller wing area was able to lift about 4,500 kg of bomb with its 5 hard points. However, I lean more towards the specs stated on the official broucher are again correct, which is 2721kg.
Regarding to the video clip that user @Radonsider linked, I don't understand Turkish, but what I have gathered by using a translator is that Mr Kotil said that the trainer will make you carry 5 (tonnes?). I am pretty sure he didn't specifiy whether if it means MTOW (maximum take-off weight) or payload or even the empty weight of the advanced jet trainer itself. Again, I don't speak Turkish so correct me if Kotil said something like MTOW.
For a reference, Boeing-Saab T-7A which is also a newly developed AJT with the same engine is rumoured to have MTOW of about 5,500 kg as well.
Turks you are quoting here knows how to speak Turkish and can understand very well what person speaking in their own language meant. Therefore, taking the lowest figures published 4-5 years ago and spreading disinformation about Hürjet project based on them, rather than official statements and updated figures, spoils the nature of healty discussion here. Therefore, it would be best to respect what you have been told about project and wait for the result of project instead of taking the old figures that suit your agenda.