Two square fields: one has area 1 hectare (10,000 m^2). The other square’s side is larger by 1%. Find the difference in their areas (in square meters).

Introduction / Context:When side length scales, area scales with the square of that factor. If the side increases by 1%, the area multiplies by (1.01)^2. The difference from the original area is then the “excess” due to squaring the side factor.

Given Data / Assumptions:

• Area of square S1 = 1 hectare = 10,000 m^2
• Side of S2 is 1% larger ⇒ area factor = (1.01)^2 = 1.0201

Concept / Approach:Compute area of the larger square S2 = 1.0201 × 10,000 = 10,201 m^2. The difference S2 − S1 equals 201 m^2, which is the required answer.

Step-by-Step Solution:S2 area = 10,000 × 1.0201 = 10,201 m^2Difference = 10,201 − 10,000 = 201 m^2

Verification / Alternative check:Approximation: doubling 1% linearly would suggest ~2% area increase; exact value is 2.01%, which on 10,000 yields 201 — matching the computation.

Why Other Options Are Wrong:100 and 200 m^2 reflect 1% or 2% approximations without compounding; 101 m^2 mixes percentage of side with area incorrectly.

Common Pitfalls:Adding percentages linearly for area; remember area depends on side squared, so apply the square of the scale factor.

Final Answer:201 sq. metres