A dog has a leash on that is 4 meters long. What is the total area of the space where the dog can travel?

There is no limit to the area that the dog can access and explore. It can go anywhere it wants to, and simply drag the leash behind. My dogs do it all the time. Now if you were to fasten the free end if the leash to a stake in the ground, then the situation would be a completely different one. Then the dog would be restricted to the circle centered at the stake with radius=4 meters. The area of such a circle is 16 pi square meters.