The situation described is shown below:
Now, from this picture we notice that the area of the base of the large rectangle is:
[tex]2x+9[/tex]
while its height is:
[tex]2x+5[/tex]
The area then will be given as:
[tex]\begin{gathered} f(x)=(2x+9)(2x+5) \\ =4x^2+10x+18x+45 \\ =4x^2+28x+45 \end{gathered}[/tex]
Therefore the function we are looking for is:
[tex]f(x)=4x^2+28x+45[/tex]
