Crossing a square field diagonally at 4 km/h:\nA person walks at 4 km/h and crosses a square field along its diagonal in 3 minutes (interpreting the time unit as minutes per standard usage). Find the area of the field in square metres.

Introduction / Context:
We relate uniform speed to distance covered along the diagonal of a square, then recover the side and compute area. The original “3 meters” appears inconsistent with a speed in km/h; under Recovery-First, we repair it to “3 minutes,” a standard formulation.

Given Data / Assumptions:

• Speed v = 4 km/h = 4000 m/60 min = 66.666… m/min.
• Time t = 3 min.
• Distance along diagonal d = v * t.

Concept / Approach:
For a square, area = (diagonal^2)/2. Compute diagonal from speed and time, then area.

Step-by-Step Solution:

Verification / Alternative check:
Side s = d/√2 ≈ 141.421 m; s^2 ≈ 20000 sq m as above.

Why Other Options Are Wrong:
10000, 30000, 40000 do not satisfy the diagonal–area relationship for the given speed and time.

Common Pitfalls:
Not converting km/h to m/min; treating the inconsistent “3 meters” literally, which breaks dimensional consistency.

Final Answer:
20000.