Billy the goat is tied to the corner of Patty�s barn. The barn is 20 x 40 feet, and the rope is 50 feet long. No trees or other obstructions are in the way. What is the available area of grass that Billy can eat? (Draw a good picture of this area first.)

Billy’s (unchewable) rope is anchored at B.

He can range through

¾ of a circle, radius 50,

¼ of a circle, radius 30, and

¼ of a circle, radius 10.

¾(50)

= (1875 + 225 + 25)

= 2125 ≈ 6676 ft

He can range through

¾ of a circle, radius 50,

¼ of a circle, radius 30, and

¼ of a circle, radius 10.

¾(50)

^{2}+ ¼(30^{2}) + ¼(10^{2})= (1875 + 225 + 25)

= 2125 ≈ 6676 ft

^{2}.This is about the same as a square 82 feet on a side or a bit more than 8 times the area of the barn.