Question

A metric chain of nominal length 20 m is found to be 20.2 m long and using it an area of 100 hectares is computed. The true area is

• A. 98.02 hectares
• B. 102.01 hectares
• C. 100.00 hectares
• D. 101.01 hectares

Hint:

When a chain is longer than its nominal length, every measured distance is recorded too short, and so the computed area is smaller than the true area. The correction uses the ratio of true to nominal chain length.

Answer 1

The Correct Option is B

Concept:
When a chain is longer than its nominal length, every measured distance is recorded too short, and so the computed area is smaller than the true area. The correction uses the ratio of true to nominal chain length.

Step 1:
The correct area is found from \[ \text{True area} = \left(\frac{L'}{L}\right)^2 \times \text{measured area} \] where \(L'\) is the incorrect (actual) chain length and \(L\) is the nominal length.

Step 2:
Substituting \(L' = 20.2\) m, \(L = 20\) m and measured area = 100 hectares: \[ \text{True area} = \left(\frac{20.2}{20}\right)^2 \times 100 = (1.01)^2 \times 100 = 1.0201 \times 100 = 102.01 \text{ hectares}. \]

Answer: Option (2) — 102.01 hectares.