>I'm trying to find a relation between the area of an scalene
>triangle and its obtuse angle while keeping the base
>constant. So, lets say I have a triangle_ABC with its
>obtuse angle_ABC = 100กใ, if one increases the ange_ABC while
>keeping the base (segment_AC) constant, the area gets
>smaller.

The area does not solely depend on the angle ABC. For example, you can reduce the area to zero without changing the angle, but only the altitude. The vertex B in this case remains on a circular arc ABC while approaching one of the ends (A or C.)

>What can I use to state the relation between the angle_ABC
>and the area?

Unless you take into account some other parameter, like the altitude from B, the best you can do is establish an inequality for the are, say,

Area(ABC) <= (b/2)2 × cot(β/2) / 2,

where b is the base and β is the angle ABC. The estimate is exact for isosceles triangles.