SOLUTION: A cow is tied to the long side of a barn 10 feet from the corner. The rope being used to tie the cow to the barn is 21 feet long. The barn measures 11 feet wide and 28 feet long,

Question 188426: A cow is tied to the long side of a barn 10 feet from the corner. The rope being used to tie the cow to the barn is 21 feet long. The barn measures 11 feet wide and 28 feet long, what is the total area of the space in which the cow can graze?
Please explain and write out your detailed answer.
Thanks!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The cow is 10 feet from the corner, so once he gets to that corner of the barn, he has 11 feet (21 - 10) of rope left with which to go around the corner. Since he is tied 10 feet from one corner of a 28 foot barn, he has 18 feet to go to get to the other corner, leaving him 3 feet (21 - 18) with which to go around the corner.

You have a 21 foot radius semi-circle, an 11 foot radius quarter circle, and a 3 foot radius quarter circle. Compute the area of each and add them together to get the total.

Use:

so the area of a semi-circle is:

and the area of a quarter-circle is:

John

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