A 30 m chain used for a survey was found to be 30.10 m at the beginning and 30.30 m at the end of the work. The area of the plan drawn to a scale of 1 cm = 8 m was measured with the help of a planimeter and was found to be 42.50 sq. cm. What is the true area of the field?

Option 1: 2890.9 m²

Option 2: 2567.0 m²

Option 3: 3456.4 m²

Option 4: 2756.4 m²

Correct Answer

Option 4: 2754.4 m²

Solution For A 30 m chain used for a survey was found to be 30.10 m

Concept Behind this solution

True Area = (L’/L)² * 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:

Data Given is:

• L’₁ = 30.10 m,
• L’₂ = 8 m,
• L = 30 m,
• Scale = 1cm:8m
• Area of Plan = 42.50 sq.cm.

Now Here Area of Field = 42.50 x 8² = 2720 sq. m.

We know that L’ = (L’₁+L’₂)/2

L’ = (30.10 + 30.30)/2

L’ = 30.20 m

We know that, True Area = (L’/L)² * Measured Area

True Area = (30.20/30)² * 2720

True Area of Field = 2756.4 m²