Measuring Pastures: Math Task

In Round County, all pasture land is formed by circles or partial circles connected together.  For example, Pasture A is made from three half circles, as seen on this map:

Pasture A

  1. Compare Pasture A with Pasture B, pictured below. 

Pasture B


  1. Which of the two pastures has a greater area?  Explain (provide a convincing mathematical explanation).


  1. Each pasture requires fencing that follows the curve of the outside of the pasture.  Which pasture requires more fencing--that is, which one has the larger perimeter?  Explain (provide a convincing mathematical explanation).


  1. Pasture C is shown below.  

Pasture C


  1. How much fencing does Pasture C require?  Explain. 



  1. How does the amount of fencing required for Pasture C compare to that required for Pastures A and B?  Explain why this relationship exists.



  1. What is the area of Pasture C?  Explain.



  1. Pasture D is shown below.  

Pasture D


  1. Predict (before calculating) the amount of fencing needed for Pasture D.  Explain how you made your prediction. 



  1. Check your prediction by calculating how much fencing is required. 




Pasture E is shown below.


Pasture E



  1. Describe two ways to compute the exact area of Pasture E.  Explain each method.



  1. How much fencing does Pasture E require?  Explain.


© 2008 by Education Development Center, Inc. from The Fostering Geometric Thinking Toolkit. Portsmouth, NH: Heinemann. Reproduced with permission.