Question 145856
Drop the altitude and find point D on AC. D cuts AC into two segments. 

ABD has a side of 6 and A at 45. So AD is also 6.
BDC has a side 6 with C at 60. So DC is 6 / tan(60) = 3.46

AC = AD+DC = 6+3.46 = 9.46

area of ABC is bh/2 = 6*9.46/2 = 28.4 in^2