Final answer:
The area of the park is 15,360 sq. m.
Step-by-step explanation:
To find the area of the park, we need to first determine the dimensions of the park. Let's assume that the length of the park is 3x and the breadth is 2x, as given in the problem.
The man completes one round of the park in 8 minutes, which is equivalent to 8/60 = 1/7 hours. The speed of the man is 12 km/hr, so the distance covered in one round is 12 * (1/7) = 12/7 km.
The perimeter of a rectangular park with length 3x and breadth 2x is given by P = 2(3x + 2x) = 2(5x) = 10x.
Since the distance covered in one round is equal to the perimeter of the park, we have 10x = 12/7 km. Solving for x, we get x = (12/7) / 10 = 12/70 = 6/35 km.
The area of the park is given by A = length * breadth = (3x) * (2x) = 6x^2. Substituting the value of x, we get A = 6 * (6/35)^2 km^2 = 6 * 36/1225 km^2.
Converting the area to square meters, we know that 1 km^2 = 1000000 m^2. Therefore, the area of the park in square meters is A = 6 * 36/1225 * (1000000) m^2 = 15,360 m^2.