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40 m2\text{40 m}^2

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Question: A lawn 10 m by 8 m is surrounded by a path 1 m wide. Find the area of the path.

  1. Find the area of the lawn.

    The lawn is rectangular with a length of 10 m and a width of 8 m.
    Area of a rectangle = length ×\times width

    Area of lawn=10 m×8 m=80 m2\text{Area of lawn} = 10 \text{ m} \times 8 \text{ m} = 80 \text{ m}^2
  2. Find the dimensions of the lawn including the path.

    The path is 1 m wide around the entire lawn.
    New length = original length + 2 ×\times path width
    New width = original width + 2 ×\times path width

    New length=10 m+(2×1 m)=10 m+2 m=12 m\text{New length} = 10 \text{ m} + (2 \times 1 \text{ m}) = 10 \text{ m} + 2 \text{ m} = 12 \text{ m} New width=8 m+(2×1 m)=8 m+2 m=10 m\text{New width} = 8 \text{ m} + (2 \times 1 \text{ m}) = 8 \text{ m} + 2 \text{ m} = 10 \text{ m}
  3. Find the area of the lawn including the path.

    Total area (lawn + path)=12 m×10 m=120 m2\text{Total area (lawn + path)} = 12 \text{ m} \times 10 \text{ m} = 120 \text{ m}^2
  4. Find the area of the path.

    Area of path = Total area (lawn + path) - Area of lawn

    Area of path=120 m2−80 m2=40 m2\text{Area of path} = 120 \text{ m}^2 - 80 \text{ m}^2 = 40 \text{ m}^2

    The area of the path is: 40 m2\text{40 m}^2

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