#### glewlwyd-gafaelfawr

##### New member

- Joined
- Jul 28, 2021

- Messages
- 6

Q: A farmer ties a horse to a building on a 50 foot lead. The building measures 20 feet by 20 feet (floor). What is the maximum area the horse can use for grazing? If there are regions you can't find the area of, provide as good an estimate as you can. Assume the horse is tied to a corner outside the building, cannot get in, and that the building is not grazing area. (Remember, this will be based on parts of circles, no other shapes...the horse's rope will only get shorter when he tries to go around the building...)

1. How much of the 50-foot circle can the horse reach without getting interrupted by the building? What is that area?

A: So, since the radius (the lead) is 50, the area of the whole circle is 7853.98? And since it's only the 50-foot circle, I gotta remove the quarter part, 7853.98/4 = 1963.495, so 7853.98 - 1963.495??? I'm dying. 5890.485. Is that right?

2. Assume the horse has grazed all of the grass in the area covered by #1 and continues on around the building. What is the new radius when the rope is interrupted by the building? What is that area covered using this new radius of rope before the rope is interrupted by the building again?

A: Ok, I have no idea. This might as well be Greek because that's as much sense as it makes to me. Can someone please explain how this works to me in simple terms, please? What do they mean by the radius when the rope is interrupted? I can't wrap my dumb head around this at all. 'Course, I have no idea about the rest of the questions either.

3. What if the horse had gone around the building the other way. What would the new radius have been when the rope was interrupted by the building? What is that area covered using this new radius of rope before the rope is interrupted by the building again?

4. The areas you found in 7 and 8 overlap each other. How much do they overlap? What *approximate* shape do they make? What is that area?

5. What is the total area the horse can graze using your calculations from #1-4?

Thanks a bunch!