My grandson's high school trigonometry teacher
posed him a fun geometry problem: A cow is tethered by a 50 ft. rope
to one corner of a 10 foot square barn. What is the area the cow can
graze? Dougy and I worked on it for about three days and found the
answer. Can you figure it out? What approach would you use? What
happens at the corners? It helps to have a grasp of high school
math and geometry. Yes, you can use your scientific calculator.
The length of rope and dimensions of barn are immaterial, the
process is the same for any numbers.
As I looked
through the internet to check our solution, I found several
variations on the theme, and I decided to come up with a general
solution to be used with any regular polygon. Some examples are
given on the conclusions page. For this answer and process go to the