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To solve this problem, we can use the formula for the area of a sector and the formula for arc length.

### Given:
- Area of the sector (\( A \)) = 200 square feet
- Radius of the circle (\( r \)) = 10 feet

### Step 1: Find the central angle \( \theta \)
The formula for the area of a sector is given by:

\[
A = \frac{1}{2} r^2 \theta
\]

where:
- \( A \) is the area of the sector,
- \( r \) is the radius of the circle, and
- \( \theta \) is the central angle in radians.

Substitute the given values into the formula:

\[
200 = \frac{1}{2} \times 10^2 \times \theta
\]

Simplify the equation:

\[
200 = 50 \times \theta
\]

Solve for \( \theta \):

\[
\theta = \frac{200}{50} = 4 \text{ radians}
\]

### Step 2: Find the arc length
The formula for the arc length (\( s \)) is:

\[
s = r \times \theta
\]

Substitute the values of \( r \) and \( \theta \):

\[
s = 10 \times 4 = 40 \text{ feet}
\]

### Final Answer:
The arc length of the sector is **40 feet**.

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Would you like further details or have any questions? 

Here are some related questions for further practice:
1. How do you convert radians to degrees, and what is the central angle in degrees?
2. If the radius of the circle were doubled, what would be the new arc length?
3. How does the area of a sector change if the central angle is halved?
4. What is the circumference of the entire circle with a radius of 10 feet?
5. If the radius were halved, what would be the new area of the sector with the same central angle?

**Tip:** Understanding the relationship between the area of a sector and the arc length can help in solving similar problems quickly.

A circular sector has an area of 200 ft². The radius of the circle is 10 feet. What is the arc length of the sector?

Learn how to calculate the arc length of a circular sector with an area of 200 ft² and a radius of 10 feet. This problem involves key geometric concepts such as the area of a sector, radians, and arc length. Suitable for students in Grades 10-12.

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