A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 12 meters long, and the other end is tied to the midpoint of one of the long sides of the building. Find the total area of the region that the dog can reach (not including the inside of the building), in square meters.
Draw yourself a picture
the dog will have a full semicircle on the long side of the building radius 12 m area = 1/2 pi 122
when pooper gets to the edge of either end of the building rope will be 3m shorter
it will have two quarter circles radius 9 m 1/2 pi 92
then when slobber-dog gets to the back edge of the building rope will be 3 + 4 m shorter
two quarter circles radius 5 1/2 pi 52