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The problem asks to find the area of the blue shaded region in a circle, where a sector with a central angle of \(150^\circ\) is shaded, and the radius of the circle is 7 cm. 

### Step-by-Step Solution:

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

   \[
   A_{\text{circle}} = \pi r^2
   \]

   Where \(r = 7\) cm, so:

   \[
   A_{\text{circle}} = \pi \times 7^2 = \pi \times 49 \approx 153.94 \, \text{cm}^2
   \]

2. **Area of the sector:**
   The area of a sector is given by the formula:

   \[
   A_{\text{sector}} = \frac{\theta}{360^\circ} \times A_{\text{circle}}
   \]

   Where \(\theta = 150^\circ\). So:

   \[
   A_{\text{sector}} = \frac{150}{360} \times 153.94 \approx 64.14 \, \text{cm}^2
   \]

3. **Subtract the white region (sector) from the total circle area:**
   The white region (which is a sector) has already been calculated. Since the blue region consists of the remainder of the circle:

   \[
   A_{\text{blue shaded region}} = A_{\text{circle}} - A_{\text{sector}} = 153.94 - 64.14 \approx 89.8 \, \text{cm}^2
   \]

### Final Answer:
The area of the blue shaded region is approximately **89.8 cm²**.

Would you like more details or have any questions?

Here are some related questions for further practice:
1. How do you find the area of a sector with a different angle?
2. How would you calculate the area of a circle if the radius was doubled?
3. What is the formula for finding the circumference of a circle?
4. How would you find the perimeter of the shaded region?
5. What if the angle was given in radians instead of degrees?

**Tip:** Always ensure your angle is in the correct units (degrees or radians) before applying it to sector area formulas.

Find the area of the blue shaded region in a circle where a sector with a central angle of 150° is shaded, and the radius of the circle is 7 cm.

Learn how to find the area of the blue shaded region in a circle where a sector with a 150° angle is given. This problem involves using the circle area formula πr² and the sector area formula. Suitable for students in Grades 7-9, with step-by-step instructions provided.

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