The Tethered Goat Problem


Laura Kimbel





Let's think about the goat being attached to a zipline. The line is 92 ft long, but his rope that is attached to the zip line is 76.7 ft long. Let's now investigate the total area that he can graze.


The figure above shows the total area the goat can graze, no matter where he is tethered. Let's now break this down into sections and find the total area based on the above measurements.



For Part I, let's look at the top portion:



Part II consists of the middle rectangle:



Now let's look at the final portion of the grazing area.



Now we can combine the areas for all 3 portions of the field to come up with a total area that the goat could potentially graze.

7924.1 + 14,112.8 + 6343.2 = 28,380.1 square feet

That's a happy goat!