Question

Write a function rule for the area of a triangle whose base is 4 ft more than the height. What is the area of the triangle when its height is 6 ft?

Answer 1

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 = $\frac{1}{2}$ × height  × base

                          F (a) =  $\frac{1}{2}$ × H × ( 4ft + H ft)

Or,                      F (a) =  $\frac{1}{2}$ × ( 4H + H² )

Now,   here Area is function of height ,

So ,                    F'(a) = $\frac{1}{2}$(4 + 2H)

Hence Area as function of H ,

                          F'(a) = 2 +H

Now For height = 6 ft

Area of triangle = $\frac{1}{2}$ × height × base

                          = $\frac{1}{2}$ × H × ( 4ft + H ft)

                          = $\frac{1}{2}$ × ( 4H + H² )

                          =  $\frac{1}{2}$ × ( 24 + 36 )

                          = $\frac{1}{2}$ × ( 60 )

                          = 30 ft²

Hence Area of triangle with height 6ft = 30 ft²      Answer