Question

The area of a rectangular field was measured using a 30 m survey chain, which was later found to be 5 cm short. If the length and width of the field measured using this chain were 542 m and 554 m, respectively, the true area of the field in ha is _____. \textit{[Round off to two decimal places]}

Hint:

When measuring land area, corrections for measurement errors due to short chains should be applied to obtain the true area.

Answer 1

Correct Answer: 29.9

The true length and width of the field can be calculated by correcting for the shortness of the chain. The correction factor is calculated as: \[ \text{Correction} = \frac{5 \, \text{cm}}{30 \, \text{m}} = 0.00167 \, \text{(short per meter)}. \] Thus, the corrected length and width are: \[ \text{Corrected length} = 542 + (542 \times 0.00167) = 542 + 0.905 = 542.91 \, \text{m}. \] \[ \text{Corrected width} = 554 + (554 \times 0.00167) = 554 + 0.925 = 554.93 \, \text{m}. \] Now, calculate the true area: \[ \text{True area} = \frac{\text{Corrected length} \times \text{Corrected width}}{10000} = \frac{542.91 \times 554.93}{10000} \approx 29.94 \, \text{ha}. \] Thus, the true area of the field is approximately \( \boxed{29.90} \, \text{ha} \) (rounded to two decimal places).