My grandson's high school trigonometry teacher
posed him a fun geometry problem: A goat is tethered by a 50 ft. rope
to one corner of a 10 foot square barn. What is the area the goat can
graze? Dougy and I worked on it for about three hours 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.
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 start with Step 1