Take a look at these 2 figures-
Figure A is the right way to go about this. I just drew a perpendicular from the angle 105 to the base. This will give you one 30-60-90 triangle and one 45-45-90 triangle. You can easily find the area then
Figure B is the figure that goes by your approach, firstly this is not a 30-60-90 triangle you see. The triangle with the perpendicular has angles 15-90-75 which don’t have any side ratios like 30-60-90 or 45-45-90 unless Trigonometry is used so because we have the side ratios present for figure A approach that is a better way to solve it.
Hope it makes sense now
