Can you find your lost dog

Geometry Level pending

The walk is one of the most important activities you can share with your dog. Assume that you are walking your dog on a straight road as shown in the above figure. At point 0, you left your dog unattended for one hour, the dog can walk along the road at speed of 8 km/h or go through the side field at speed of 4 km/h. How far your dog run is just a function of how far its legs will carry it. Can you determine the domain in which you may find your dog after one hour? Report your answer to this problem as the area of this domain to the nearest 3 decimal places.

Hint : Assume that the domain's boundaries are x-axis, y-axis, and the maximum distances can your dog reach inside the field.

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