Shantanu cycles along the boundary of a square field ABCD starting at corner A. After 1/2 hour he reaches corner C (the corner diagonally opposite A) by following the boundary. If his cycling speed is 16 km/h, what is the area of the square field?

Introduction / Context:
On a square, traveling from one corner to the diagonally opposite corner along the boundary equals half the perimeter. If the traveler’s speed and the time are known, the boundary distance is known, from which we find the side and thus the area.

Given Data / Assumptions:

• Time = 1/2 h.
• Speed = 16 km/h ⇒ distance covered = 16 * 1/2 = 8 km.
• Boundary distance from A to opposite corner C = half the perimeter = 2s, where s is the side of the square.

Concept / Approach:
Since 2s = 8 km ⇒ s = 4 km. Area of square = s^2 = 16 sq km. Compare to options.

Step-by-Step Solution:

Verification / Alternative check:
Perimeter would be 4s = 16 km; half is 8 km, exactly what he traveled in 1/2 h at 16 km/h.

Why Other Options Are Wrong:
8, 9, or 19 sq km do not match the computed 16 sq km. Hence “None of the above” is correct.

Common Pitfalls:
Confusing boundary travel with the straight diagonal (which is s√2, not 2s) or misusing time–speed–distance.

Final Answer:
None of the above (actual area = 16 sq km)