The fountain is depicted by the white circle in the picture. The surrounding walkway is depicted by the grey areas.
From the sketch shown above, the semi-circle inscribed in the rectangle is one half of the fountain. We shall calculate the area of the semi-circle and subtract this from the area of the rectangle.
The area of the rectangle is;
[tex]\begin{gathered} \text{Area}=l\times w \\ \text{Area}=30\times42.5 \\ \text{Area}=1275ft^2 \\ \text{The area of the semicircle is,} \\ \text{Area=}\frac{1}{2}(\pi\times r^2) \\ \text{The diameter is 18 ft, and therefore the radius is 9 ft} \\ \text{Area}=\frac{1}{2}(3.14\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=\frac{1}{2}(254.34) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]
Therefore, the area of the shaded region would be,
Area = 1275 - 127.17
Area = 1147.83
Next step is to calculate the other half of the figure (the right side), as follows;
Observe that the outer semi-circle is the shaded region while the inner one is the white portion.
The area is
[tex]\begin{gathered} \text{Shaded region;} \\ \text{Area}=\frac{1}{2}(\pi\times r^2) \\ \text{Area}=\frac{1}{2}(3.14\times15^2) \\ \text{Area}=\frac{1}{2}(3.14\times225) \\ \text{Area}=\frac{1}{2}(706.5) \\ \text{Area}=353.25ft^2 \\ \text{White region;} \\ \text{Area}=\frac{1}{2}(\pi\times9^2) \\ \text{Area}=\frac{1}{2}(3.14\times81) \\ \text{Area}=127.17ft^2 \end{gathered}[/tex]
The area of the shaded region is;
Area = 353.25 - 127.17
Area = 226.38
Therefore the total area of the walkway surrounding the fountain is;
Area = 1147.83 + 226.38
Area = 1374.21
Area = 1,374 feet squared (rounded to the nearest foot)
