Question
A rectangular field is 80 m long and 60 m wide. A path 5 m wide runs around the outside of the field. Find the area of the path.
Solution — Step by Step
The path goes around the outside of the field, so it adds 5 m on each side.
- Outer length = m (5 m added on each end)
- Outer width = m
Why This Works
The path is the region between the outer boundary (field + path) and the inner boundary (field alone). Subtracting the inner area from the outer area gives only the path area. This “ring” or “frame” approach works for any uniform border around a rectangle.
Alternative Method — Direct Calculation
The path can be divided into four rectangles (two along the length, two along the width) and four corner squares.
Two lengthwise strips: m²
Two widthwise strips: m²
Four corner squares: m²
Total: m² ✓
The subtraction method is faster; this verification method is useful for understanding the geometry.
Common Mistake
A very common error is adding only 5 m (not 10 m) to each dimension. The path is on BOTH sides of the rectangle. So the outer length is m, not m. Similarly, the outer width is m. Forgetting to add the path width on both sides accounts for the majority of wrong answers in this type of problem.