Irregular boundary area by the trapezoidal rule and by Simpson's one-third rule
Nine offsets to a meandering creek bank at 25 ft intervals, reduced two ways. The two rules differ by 22.5 ft², and the reason they differ is the reason to prefer one of them.
Recall· about 16 minutes by hand· 5 steps
Given
A traverse line runs along the upland side of a parcel. Perpendicular offsets were taken from that line to the top of a creek bank at a constant interval of d = 25.00 ft.
Nine offsets were taken, giving eight intervals: 12.4, 18.7, 24.2, 27.9, 29.5, 26.8, 21.3, 15.6, 10.2 ft, in order along the line.
Offsets are recorded to 0.1 ft, which is as well as the top of bank can be identified.
The strip between the traverse line and the bank is to be added to a parcel area computed by coordinates.
Required
The strip area by the trapezoidal rule.
The strip area by Simpson's one-third rule.
Which value should be carried forward, and why they differ.
Work it through yourself before reading on - the solution below shows every step, so there is no way to skim it without giving the answer away.
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