Part A.
From the given figure, we know that the bookshelf area is

and the area of the entire library is the sum of the bookshelf area plus the reading area. This last area is given by

becuase this area has a square shape. By combining similar terms, we can rewritte this area as follows

By expanding this result, we get

Now ,we will add this area with the bookshelf area in order to get the entire area of the library, that is,

then, by combining similar terms, the area of the entire library is

Part B.
Because the area of the entire library has a rectangular shape and its area is given by

with the width given by

and length
