I have a formula. Assuming b and h are the base and height of the triangle:

b^2 = 32h - 2h^2

Substitute that into the area formula and then use derivatives, blah blah you should be able to do that part.

I do not know if this is correct. I got this by drawing the picture and making different triangles. I noticed something in the triangles I made that looked good but I didn't have time to go check, because it's almost bedtime. I hope this gets you on the right track, though. What I do know is that your first method looks completely wrong.

This is as much you get from me by whining for Unne first instead your friendly neighborhood math graduate.