Surveying correction for area due to erroneous chain length If the area of a plan has been computed from measurements taken with an erroneous chain (too long or too short), how should the accurate (true) area be obtained from the calculated area? Select the correct correction factor and relation.

Introduction / Context:
In chain surveying and all distance-based mapping, any uniform error in the measuring length (for example, a chain that is too long or too short) propagates into the plotted lengths and hence the computed area. Because areas scale with the square of linear dimensions, the correct area must be obtained by applying a squared scale factor. This question tests whether you can recall and apply the correct correction relation for area when the chain length is erroneous.

Given Data / Assumptions:

• All distances in the survey were measured with the same erroneous chain length, denoted L_err.
• The correct (standard) chain length is L_true.
• The area has been computed from the plotted plan using the uncorrected distances.

Concept / Approach:

If every measured length is scaled by a factor k = L_err / L_true relative to truth, then each linear dimension on the plan is off by k. Since area depends on the product of two independent linear dimensions, the computed area is off by k^2. To recover the true area, divide by k^2, or equivalently multiply by (L_true / L_err)^2.

Step-by-Step Solution:

Verification / Alternative check:

Check with a square plot: if each side is over-measured by 2%, k = 1.02. Area error ≈ 1.02^2 ≈ 1.0404 (about 4.04%). Correcting by (1/1.02)^2 restores the true area, matching the squared law expectation.

Why Other Options Are Wrong:

Option B inverts the factor, worsening the error. Options C and D use a first-power factor, which is appropriate for linear quantities but not for areas.

Common Pitfalls:

Applying only a single power of the correction factor to an area; forgetting to keep the ratio in the correct order (true over erroneous) when correcting results.

Final Answer:

True area = Calculated area * (true chain length / erroneous chain length)^2