A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 4 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.
+14917 A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 4 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.
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\(A=\frac{1}{2}\cdot \pi \cdot r^2+\frac{2}{4}\cdot (r-\frac{6m}{2})^2\cdot \pi\)
\(r=4m\)
\(A=\frac{1}{2}\cdot \pi \cdot ({\color{BrickRed}4m})^2+\frac{2}{4}\cdot ({\color{BrickRed}4m}-\frac{\color{BrickRed}6m}{2})^2\cdot \pi\)
\(A=26.704\ m^2\)
The region that the dog can reach is 26.704 square meters.
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