Let's solve the problem step-by-step:
1. Understand the dimensions of the garden and sidewalk:
- The diameter of the garden is given as 18 feet.
- The width of the sidewalk around the garden is 2 feet.
2. Calculate the radius of the garden:
- The radius of a circle is half of its diameter.
- Therefore, the radius of the garden is [tex]\( \frac{18 \text{ feet}}{2} = 9 \text{ feet} \)[/tex].
3. Calculate the radius of the overall area including the sidewalk:
- The sidewalk extends 2 feet beyond the edge of the garden.
- Therefore, the radius of the total area including the sidewalk is [tex]\( 9 \text{ feet} + 2 \text{ feet} = 11 \text{ feet} \)[/tex].
4. Calculate the area of the garden:
- The formula for the area of a circle is [tex]\( \pi \times \text{radius}^2 \)[/tex].
- Using [tex]\(\pi \approx 3.14\)[/tex] and the radius of the garden (9 feet), the area of the garden is:
[tex]\[
\pi \times (9 \text{ feet})^2 = 3.14 \times 81 \text{ square feet} = 254.34 \text{ square feet}
\][/tex]
5. Calculate the area of the total region including the sidewalk:
- Using [tex]\(\pi \approx 3.14\)[/tex] and the radius of the total region (11 feet), the area of the total region is:
[tex]\[
\pi \times (11 \text{ feet})^2 = 3.14 \times 121 \text{ square feet} = 379.94 \text{ square feet}
\][/tex]
6. Calculate the area of the sidewalk alone:
- The area of the sidewalk is the area of the total region minus the area of the garden.
- Therefore, the sidewalk area is:
[tex]\[
379.94 \text{ square feet} - 254.34 \text{ square feet} = 125.6 \text{ square feet}
\][/tex]
So, the area of the sidewalk is [tex]\( 125.6 \)[/tex] square feet.
