Consider the following diagram,
Let 'y' be the side of the garden. And 'x' be the side of the square formed by the walkway.
Given that the garden is a square with perimeter 260 feet,
[tex]\begin{gathered} \text{Perimeter}=260 \\ 4y=260 \\ y=65 \end{gathered}[/tex]From the above diagram, it can be observed that,
[tex]\begin{gathered} x=4+y+4 \\ x=8+y \\ x=8+65 \\ x=73 \end{gathered}[/tex]Consider that the area of a square is given by,
[tex]\text{Area of square}=Side^2[/tex]The area of the inner square i.e. garden will be,
[tex]\begin{gathered} A_i=y^2 \\ A_i=65^2 \\ A_i=4225 \end{gathered}[/tex]The area of the outer square will be,
[tex]\begin{gathered} A_o=x^2 \\ A_o=73^2 \\ A_o=5329 \end{gathered}[/tex]The difference between the area will give the area of the walkway (A), that can be calculated as,
[tex]\begin{gathered} A=A_o-A_i \\ A=5329-4225 \\ A=1104 \end{gathered}[/tex]Thus, the area of the walkway is 1104 square feet.
