Area of the path?
A hard-level "Area" problem.For any path of constant width — circular, square or wiggly — the area is "length of the centre line × width". Faster and safer than subtracting.
GivenA round pond of radius 10 m with a 2 m wide path around it / π = 3.14
Hints
- Start with the direct route. The outer circle has radius 10 + 2 = 12 m, so its area is 452.16 m².
- The pond (inner circle) is 10 × 10 × 3.14 = 314 m². Subtract, and the path is 138.16 m².
- Now a completely different view. Redraw, and think about the dashed circle running right down the middle of the path. Its radius is 10 + 2 ÷ 2 = 11 m.
- That circle's circumference is 2 × 11 × 3.14 = 69.08 m. Now imagine cutting the path along this line and straightening it out.
- Straightened out it is a long thin rectangle, 69.08 m by 2 m. The inside edge shrinks and the outside stretches, but the middle line is neither, so its length is unchanged.
- 69.08 × 2 = 138.16 m² — exactly the same answer as the subtraction gave.
Answer 138.16m²
More "Area" problems
- Area of the inner triangle?
- Area of triangle DOA?
- Area of quadrilateral ABCD?
- Area of the overlap?
- Total area of the two crescents?
- Area swept by the square?