Avery planned a circular garden and path as shown below. The radius of the garden is 4 feet and the path around the garden is 2 feet wide. What is the total area of the garden and path? (Use 3.14 for & and round to the nearest tenth.)

1 answer

To find the total area of the garden and the path, we first need to calculate the total radius of the garden plus the path.

  1. Calculate the radius of the garden:

    • Given the Garden's radius = 4 feet.
  2. Calculate the width of the path:

    • The path around the garden is 2 feet wide.
  3. Calculate the total radius (garden + path): \[ \text{Total radius} = \text{Garden radius} + \text{Path width} = 4 \text{ feet} + 2 \text{ feet} = 6 \text{ feet} \]

  4. Calculate the area of the garden (using \( \pi \approx 3.14 \)):

    • The formula for the area of a circle is \( \text{Area} = \pi r^2 \). \[ \text{Area of the garden} = 3.14 \times (4^2) = 3.14 \times 16 = 50.24 \text{ square feet} \]
  5. Calculate the area of the larger circle (garden + path): \[ \text{Area of the larger circle} = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 \text{ square feet} \]

  6. Calculate the total area of the garden and path (just the larger circle's area): The total area of the garden plus the path is the area of the larger circle: \[ \text{Total area} = \text{Area of the larger circle} = 113.04 \text{ square feet} \]

  7. Rounding to the nearest tenth: \[ \text{Total area rounded} = 113.0 \text{ square feet} \]

Thus, the total area of the garden and path is \( \boxed{113.0} \) square feet.