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

- Compare Pasture A with Pasture B, pictured below.

Pasture B

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

- 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).

- Pasture C is shown below.

Pasture C

- How much fencing does Pasture C require? Explain.

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

- What is the area of Pasture C? Explain.

- Pasture D is shown below.

Pasture D

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

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

### Extension:

Pasture E is shown below.

Pasture E

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

- How much fencing does Pasture E require? Explain.