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In the given problem, you are asked to find the shaded area of a circular sector where the radius of the circle is 17 cm and the arc length is 26 cm.

### Steps to solve:

1. **Find the central angle of the sector**:
   The arc length (\(L\)) of a sector is related to the radius (\(r\)) and the central angle (\(\theta\)) (in radians) by the formula:
   \[
   L = r \times \theta
   \]
   We can rearrange this to solve for \(\theta\):
   \[
   \theta = \frac{L}{r}
   \]
   Substituting the given values:
   \[
   \theta = \frac{26}{17} \approx 1.5294 \text{ radians}
   \]

2. **Find the area of the sector**:
   The area (\(A\)) of a sector is given by the formula:
   \[
   A = \frac{1}{2} r^2 \theta
   \]
   Substituting the known values:
   \[
   A = \frac{1}{2} \times 17^2 \times 1.5294
   \]

Let me calculate that for you.The area of the shaded sector is approximately \(221 \, \text{cm}^2\).

Would you like further details or explanations? Here are some related questions to deepen your understanding:

1. How can the area of a full circle be calculated using its radius?
2. How would the calculation change if the arc length was in degrees rather than radians?
3. Can you derive the formula for the area of a sector using basic geometry principles?
4. What if the radius of the circle was different—how would that affect the sector's area?
5. How do we find the perimeter of the sector, including the arc and straight sides?

**Tip**: Always make sure you're working in consistent units (radians or degrees) when calculating angles in geometry problems!

The radius of a circle is 17 cm. The arc length of a sector is 26 cm. Find the shaded area.

Learn how to find the shaded area of a sector where the circle has a radius of 17 cm, and the arc length is 26 cm. This problem covers key geometric concepts such as the arc length formula and sector area formula. Suitable for students in Grades 10-12.

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