Answer:
B. [tex]A(h) =3h^3 -h[/tex]
Step-by-step explanation:
Given is the figure of a trapezoid with following descriptions.
[tex] b_1=2h^2 +2[/tex]
[tex] b_2 =2h^2 +2+ 2h^2-6=4h^2 - 4[/tex]
[tex] height = h[/tex]
Now, by formula of area of trapezoid, we have:
[tex]A(h) =\frac{1}{2} (b_1+b_2)h[/tex]
[tex]A(h) =\frac{1}{2} (2h^2 +2+4h^2 - 4)h[/tex]
[tex]A(h) =\frac{1}{2} (6h^2 -2)h[/tex]
[tex]A(h) =\frac{1}{2} (6h^3 -2h)[/tex]
[tex]A(h) =\frac{1}{2} \times 2(3h^3 -h)[/tex]
[tex]A(h) =(3h^3 -h)[/tex]
[tex]A(h) =3h^3 -h[/tex]
