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In this problem, Fido is on a 17.6-foot chain that allows him to roam within half a circle around the back of the barn. The area available for Fido to roam can be calculated using the formula for the area of a circle, \( A = \pi r^2 \), where \( r \) is the radius of the circle, and then taking half of this value since he can only access half of the area.

Given:
- \( r = 17.6 \) feet
- \( \pi \approx 3.14 \)

The area of the full circle is:
\[ A = \pi r^2 = 3.14 \times (17.6)^2 \]

To find the area that Fido can actually use:
\[ A_{\text{half-circle}} = \frac{1}{2} A \]

Let's calculate the total area to the nearest tenth.Fido has approximately 486.3 square feet of area to roam.

Would you like to know more details about this calculation or have any other questions on this topic? Here are some follow-up questions you might consider:

1. How would the area change if Fido's chain were longer or shorter?
2. What if Fido were allowed to roam around the entire barn?
3. How would you calculate the perimeter of the space Fido can roam?
4. Can you explain how the formula for the area of a circle is derived?
5. What are practical applications of knowing the area of a circle in real life?

**Tip:** When calculating the area affected by a radius change, remember that the area of a circle is proportional to the square of the radius. This means small changes in the radius result in larger changes in the area.

Fido the dog is on a 17.6-ft chain that is attached to the middle of the back of a barn, as shown in the picture below. The chain does not allow him to go past either of the adjacent sides of the barn, thereby allowing him to roam all the space inside 1/2 of a circle. How much area does Fido have to roam? Use 3.14 for pi. Round your answer to the nearest tenth, but do not include 'sq ft' or 'ft^2' with your response.

Learn how to calculate the area a dog can roam when attached to a 17.6-ft chain. This problem involves finding the area of a half-circle using the formula A = πr^2, suitable for students in Grades 6-8.

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