the three medians AD BE CF of triangle ABC are concurrent at G . if angke AGC is 120 AG=8 and GC =12 what is are of abc

First thing you need to know is that medians divide the triangle into 6 parts of equal areas. So, if can find the area of any one small triangle, then the area of big triangle can be found. We know angle AGC = 180. So angle AGF would be 60 (Linear pair angles). GF is 6 and AG is 8. Now using cosine formula we can find AF, which is given by
AF^2 = 8^2 +6^2 - 2*8*6*1/2 =>AF^2 = 52. Now we know the three sides so which can used to find the area of this traingle. Using this we can find the area of big triangle.