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To find the area of the blue shaded region, we need to calculate the area of the sector corresponding to the 150° angle in the circle.

### Steps to solve:

1. **Area of the full circle**:
   The formula for the area of a circle is:

   \[
   A = \pi r^2
   \]

   Here, \( r = 6 \, \text{cm} \), so the area of the full circle is:

   \[
   A_{\text{circle}} = \pi (6)^2 = 36\pi \, \text{cm}^2
   \]

2. **Fraction of the circle occupied by the sector**:
   Since the angle of the sector is \(150^\circ\), the fraction of the circle represented by the sector is:

   \[
   \text{Fraction of circle} = \frac{150^\circ}{360^\circ} = \frac{5}{12}
   \]

3. **Area of the sector**:
   Multiply the area of the full circle by the fraction to find the area of the sector:

   \[
   A_{\text{sector}} = \frac{5}{12} \times 36\pi = 15\pi \, \text{cm}^2
   \]

4. **Final Calculation**:
   To get the numerical value, we use \( \pi \approx 3.1416 \):

   \[
   A_{\text{sector}} \approx 15 \times 3.1416 = 47.1 \, \text{cm}^2
   \]

Therefore, the area of the blue shaded region is approximately \( \boxed{47.1} \, \text{cm}^2 \).

Would you like more details, or do you have any other questions?

Here are 5 related questions to explore further:

1. How would the area change if the radius was doubled?
2. What is the area of the remaining white region in the circle?
3. How would you calculate the perimeter of the blue-shaded sector?
4. How is the formula for the area of a sector derived?
5. How does the result change if the sector angle was \(120^\circ\)?

**Tip**: Always make sure that the angle is in degrees (or radians) when applying formulas related to sectors.

Find the area of the blue shaded region in a circle with a 150° angle and a radius of 6 cm. Round to the nearest tenth.

Learn how to find the area of a blue shaded sector in a circle with a central angle of 150° and a radius of 6 cm. This problem covers key geometry concepts such as the area of a circle and sectors. Suitable for students in Grades 7-9.

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