We are given the following information
Length of rectangular deck = 12 feet
Perimeter of rectangular deck = 36 feet
Recall that the perimeter of rectangular shape is given by
[tex]P=2l+2w_{}[/tex]Where l is the length, w is the width, and P is the perimeter of the rectangle.
Let us substitute the given values and solve for width (w)
[tex]\begin{gathered} P=2l+2w_{} \\ 36=2(12)+2w_{} \\ 36=24+2w_{} \\ 36-24=2w_{} \\ 12=2w_{} \\ \frac{12}{2}=w \\ 6=w \\ w=6\: feet \end{gathered}[/tex]Therefore, the deck's width is 6 feet
Recall that the area of a rectangular shape is given by
[tex]A=l\cdot w[/tex]Where l is the length and w is the width of the rectangle.
[tex]\begin{gathered} A=l\cdot w \\ A=12\cdot6 \\ A=72\: ft^2 \end{gathered}[/tex]Therefore, the deck's area is 72 square feet.