A man walking at a speed of 3 km/h crosses a square field diagonally in 5 minutes. What is the area of the field (in m$$^2$$)?

Let the side of the square field = a

Speed of the man = 3 km/h = 3 x $$\frac{1000}{60}$$ m/min = 50 m/min

Time taken to cross the field diagonally = 5 minutes

Length of the diagonal of the square field = 50 x 5 = 250 m

$$\sqrt{2}$$a = 250

a = $$\frac{250}{\sqrt{2}}$$ m

Area of the square field = a$$^2$$

= $$\left(\frac{250}{\sqrt{2}}\right)^2$$

= $$\frac{62500}{2}$$

= 31250 m$$^2$$

Hence, the correct answer is Option A