Correct Answer - Option 3 : 2756.4 m
2
Concept:
\(\text{True area} = (\frac{L'}{L})^2 × \text{measured area}\)
Where,
L' = actual length of the chain while measuring distance = Average length of the chain while measuring,
L = true length of chain,
Calculation:
Given,
L'1 = 30.10 m, L'2 = 30.30 m, L = 30 m,
Scale = 1 cm : 8 m, area of plan = 42.50 sq. cm.
Now, Area of field = 42.50 × 82 = 2720 sq. m.
∵ We know that, \(\text{L'} = \frac{L'_1 + L'_2}{2}\)
⇒ \(\text{L'} = \frac{30.10 + 30.30}{2}\)
∴ L' = 30.20 m
∵ We know that, \(\text{True area} = (\frac{L'}{L})^2 × \text{measured area}\)
⇒ \(\text{True area} = (\frac{30.2}{30})^2 × \text{2720}\)
∴ True Area of field = 2756.4 m2