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.