One round of the park is equal to the perimeter of the park.
So, by completing one round, the cat covers a distance equal to the perimeter of the park.
Now, Distance or perimeter = speed * time
= 18 * (10/60)
= 3 km or 3000 meters
Let Length = 4x and breadth = 2x
So, Perimeter: 2 (4x + 2x) = 3000
8x + 4x = 3000
12x = 3000
x= 3000/12= 250 meters
So, Length = 4 * 250 = 1000 meters
And, Breadth = 2 * 250 = 500 meters
Area = Length * Breadth
= 1000 * 500
= 50000 sq. m.