Part 1 (Area of the Garden)
In Plan A. the garden measures 9 ft by 12 ft.
[tex]\begin{gathered} \text{Area of the garden in Plan A=}_{}9\times12 \\ =108ft^2 \end{gathered}[/tex]
In Plan B, the garden has a radius of 5 ft.
[tex]\begin{gathered} \text{Area of the garden in Plan B=}_{}\pi r^2 \\ =\pi\times5^2 \\ =25\pi ft^2 \end{gathered}[/tex]
Part 2 (Area of the Deck)
Area of the Deck = Area of the outer shape-Area of the garden
Plan A
[tex]\begin{gathered} \text{Area of the deck=}(18\times25)-108 \\ =450-108 \\ =342ft^2 \end{gathered}[/tex]
Plan B
[tex]\begin{gathered} \text{Area of the deck=(16x20)-25}\pi \\ =241.46ft^2 \end{gathered}[/tex]
Part 3
It costs $4.20 per square foot to install the deck:
[tex]\begin{gathered} \text{Cost of Plan A=342 x 4.20 =\$1436.40} \\ \text{Cost of Plan B=241.46 x 4.20 =\$1}014.13 \end{gathered}[/tex]
Part 4
It costs $1.40 per square foot to install the garden:
[tex]\begin{gathered} \text{Cost of Plan A=108 x 1.40 =\$}151.20 \\ CostofPlanB=25\pi\times\text{ 1.40 =\$1}09.96 \end{gathered}[/tex]
Part 5
We calculate the total costs
[tex]\begin{gathered} Total\; c\text{ost of Plan A=1}436.40+151.20=1587.60 \\ Cost\; of\; PlanB=1014.13+\text{1}09.96=1124.09 \end{gathered}[/tex]
We see that Plan B is less expensive by:
[tex]\begin{gathered} 1587.60-1124.09 \\ =\$463.51 \end{gathered}[/tex]
