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

Step 1: Note the data.
Nominal chain length \(L = 20\) m, actual length \(L' = 20.2\) m, computed area \(A = 100\) hectares.

Step 2: Understand the effect.
A long chain measures fewer chain lengths, so the computed area comes out smaller than the real area. The true area is therefore larger.

Step 3: Write the area correction rule.
\[ \text{True area} = \left(\frac{L'}{L}\right)^2 \times \text{Computed area} \]

Step 4: Find the length ratio squared.
\[ \frac{L'}{L} = \frac{20.2}{20} = 1.01, \qquad (1.01)^2 = 1.0201 \]

Step 5: Multiply by the computed area.
\[ \text{True area} = 1.0201 \times 100 = 102.01 \text{ hectares} \]

Step 6: State the answer.
The true area is 102.01 hectares.
\[ \boxed{102.01 \text{ hectares}} \]