Answer :
Part A.
From the given figure, we know that the bookshelf area is
[tex]20x^2+110x+120[/tex]and the area of the entire library is the sum of the bookshelf area plus the reading area. This last area is given by
[tex]A_{\text{reading}}=((x+3)+x+(x+3))^2[/tex]becuase this area has a square shape. By combining similar terms, we can rewritte this area as follows
[tex]A_{\text{reading}}=(3x+6)^2[/tex]By expanding this result, we get
[tex]A_{\text{reading}}=9x^2+36x+36[/tex]Now ,we will add this area with the bookshelf area in order to get the entire area of the library, that is,
[tex]\begin{gathered} A=A_{\text{bookshelf}}+A_{\text{reading}} \\ A=20x^2+110x+120+9x^2+36x+36 \end{gathered}[/tex]then, by combining similar terms, the area of the entire library is
[tex]A=29x^2+146x+156[/tex]Part B.
Because the area of the entire library has a rectangular shape and its area is given by
[tex]A=\text{width}\times length[/tex]with the width given by
[tex]\text{width}=3x+6[/tex]and length
[tex]\text{length}=3(5+2x)[/tex]