Question

I need to know the area of the walkway and how you got the answer

Answer 1

The problem statement asks for the area of the pool. We will assume that is an error, and that you want to fill in the table with the area of the walkway.

Consider a walkway of width w. The outside dimension of the walkway will be 2w plus the dimension of the pool (since there is a walk on either side). Thus, the outside dimensions of the pool and walkway are 9+2w and 12+2w yards.

The area of the pool and walkway will be

... total area = pool area + walkway = (9 + 2w)(12 + 2w) = 9·12 + 2w(9+12) +4w²

... total area = (9·12) + walkway = 9·12 + 42w + 4w²

Subtracting the pool area gives the area of the walkway as

... walkway = 42w + 4w² = 2w(2w+21)

Using this formula, we can fill in the table

$\begin{array}{cc}\text{width}&\text{area (yd^2) }\\0.5&22\\1.0&46\\1.5&72\\2.0&100\\N&2N(2N+21)\end{array}$