- 2075 Asoj · 4 marks
Area between boundary, offsets and base line
Short answer
Apply the trapezoidal rule to each strip of unequal width. Area = sum of (width × mean of adjacent offsets) = 396.80 m².
From the chainages and offsets given below, find the area between the boundary, the first and last offsets and base line.
| Chainage (m) | 0 | 12 | 20 | 25 | 34 | 42 | 52 |
|---|---|---|---|---|---|---|---|
| Offset (m) | 0 | 6.9 | 7.6 | 9.8 | 10.2 | 9.9 | 6.8 |
The chainages are at unequal intervals, so the area is found strip by strip with the trapezoidal rule (the strip between two offsets is a trapezium of width equal to the chainage difference).
| Strip | Width (m) | (m) | (m) | Area (m²) |
|---|---|---|---|---|
| 1 | 12.00 | 0.00 | 6.90 | 41.4000 |
| 2 | 8.00 | 6.90 | 7.60 | 58.0000 |
| 3 | 5.00 | 7.60 | 9.80 | 43.5000 |
| 4 | 9.00 | 9.80 | 10.20 | 90.0000 |
| 5 | 8.00 | 10.20 | 9.90 | 80.4000 |
| 6 | 10.00 | 9.90 | 6.80 | 83.5000 |
| Total | 396.8000 |
Check by coordinates: with the points (0,0), (52,0), (52,6.8), (42,9.9), (34,10.2), (25,9.8), (20,7.6), (12,6.9), (0,0) the formula
gives 396.800 m², the same value.
Answer: area = 396.80 m².
✓ Answer checked by Claude Opus 5.5 (high effort)
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