zoe the goat is tied by a rope to one corner of a 15m by 25m barn in the middle of a large grassy field. what area of the field can zoe graze if the rope is 30m long
Zoe can go from one side of the barn all the way to the adjacent side, making 3/4 of a circle that is 30m in radius. Once Zoe’s rope hits one of the walls, Zoe can go around the corner, but the rope has to wrap around. You subtract the length of the wall from the rope to get the radius of this curve. The curve is just 1/4 of a circle before Zoe hits the wall. So, there is the big 3/4 circle and two smaller 1/4 circles.
Area of 3/4 circle with radius 30: