https://file.aiquickdraw.com/mathbot/file/172600470743453kzsk4y.jpg

To find the area of the sector shown in the image, we use the formula for the area of a sector of a circle:

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

Where:
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

From the image:
- The radius \( r = 12 \),
- The angle \( \theta = 0.5 \, \text{rad} \).

Now, let's compute the area \( A \). 

\[
A = \frac{1}{2} \times 12^2 \times 0.5
\]

Let me calculate that for you.The area of the sector is \( 36 \, \text{square units} \).

Would you like further details or have any other questions?

Here are 5 related questions you might find interesting:
1. How do you calculate the area of a full circle?
2. What is the circumference of a circle with radius 12 units?
3. How would the area change if the angle were in degrees instead of radians?
4. What is the formula for the length of an arc of a sector?
5. How do you calculate the perimeter of a sector, including the arc length?

**Tip:** Always ensure that the angle in your formula is in radians when calculating areas or lengths related to circular sectors.

Find the area of the sector in the circle with a radius of 12 units and an angle of 0.5 radians.

Learn how to calculate the area of a sector with a radius of 12 units and an angle of 0.5 radians. This geometry problem uses the formula A = 1/2 * r^2 * θ to find the sector area. Suitable for students in Grades 8-10.

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