A man walking at the speed of 4 kmph crosses a square field diagonally in 3 minutes. The area of the field is

### Concept & Distance and Area Relation First, use the speed and time to find the total distance walked, which corresponds to the length of the diagonal. Then, use the diagonal to find the area. $$ \text{Distance} = \text{Speed} \times \text{Time} $$ $$ \text{Area of Square} = \frac{1}{2}d^2 $$ ### Step-by-Step Solution * Convert speed from kmph to m/s: $4 \text{ kmph} = 4 \times \frac{5}{18} = \frac{10}{9}$ m/s. * Convert time from minutes to seconds: $3 \text{ minutes} = 3 \times 60 = 180$ seconds. * Calculate the diagonal length (distance): $d = \frac{10}{9} \times 180 = 200$ metres. * Calculate the area using the diagonal: $\text{Area} = \frac{1}{2} \times (200)^2$. * $\text{Area} = \frac{1}{2} \times 40000 = 20000 \text{ m}^2$. ### Exam Strategy & Shortcut You can keep units simpler: $4 \text{ km/hr} = 4000 \text{ m} / 60 \text{ min}$. In 3 minutes, he covers $4000 \times \frac{3}{60} = \frac{4000}{20} = 200$ metres. $\text{Area} = \frac{200^2}{2} = 20000$. This avoids messy fractional m/s conversions. ### Common Pitfall Failing to convert units consistently (e.g., mixing kmph with minutes directly) will lead to vastly incorrect diagonal lengths. ### Final Answer Therefore, the correct answer is **20000 $m^2$**.