Since the formula for the area of a triangle is

            A = b·h

and we have the height = h = 12, we must find the base. Let the left 
part of the base be x and the right part of the base be y.



To find x, we use 

tan(60°) = 

Multiply both sides by x:

x·tan(60°) = 12

Divide both sides by tan(60°)

         x = 
         x = 6.9282


To find y, we also use 

tan(40°) = 

Multiply both sides by y:

y·tan(40°) = 12

Divide both sides by tan(40°)

         y = 
         y = 14.3010

the base = b = x + y = 6.9282 + 14.3010 = 21.2292

            A = b·h
            A = (21.2292)(12)
            A = 127.3752  

Edwin