Error propagated into a computed area from errors in two sides
A rectangular parcel measured on two sides, and the uncertainty those two measurements put into the acreage - with the fractional form of the same result as a check and the worst case as a bound.
Recall· about 14 minutes by hand· 4 steps
Given
A rectangular parcel is measured on two adjacent sides.
Side a = 248.16 ft, with a standard error of ±0.03 ft.
Side b = 412.55 ft, with a standard error of ±0.04 ft.
The two measurements were made independently - different setups, different tape settings - so their errors are uncorrelated.
The corners are square by construction and the squareness is taken as exact for this computation.
Distances in US survey feet.
Required
The area and its standard error, in square feet and in acres.
The relative precision of the area, and how it relates to the relative precisions of the two sides.
The 95 per cent uncertainty in the area.
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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