Answer:
A) Area as function of H ,
      F'(a) = 2 +H
B) Area of triangle with height 6ft = 30 ft²      
Step-by-step explanation:
Given as for a triangle , 
Let the height of triangle = H ft
And base = 4 ft + H ft
Now area of triangle =  × height  × base
 × height  × base
                           F (a) =   × H × ( 4ft + H ft)
 × H × ( 4ft + H ft)
Or,                      F (a) =   × ( 4H + H² )
 × ( 4H + H² )
Now,   here Area is function of height ,
So ,                    F'(a) =  (4 + 2H)
(4 + 2H)
 Hence Area as function of H ,
                           F'(a) = 2 +H
Now For height = 6 ft
Area of triangle =  × height × base
 × height × base
                           =  × H × ( 4ft + H ft)
 × H × ( 4ft + H ft)
                           =  × ( 4H + H² )
 × ( 4H + H² )
                           =   × ( 24 + 36 )
 × ( 24 + 36 )
                           =  × ( 60 )
 × ( 60 )
                           = 30 ft²
Hence Area of triangle with height 6ft = 30 ft²      Answer