What is the formula for the perimeter of a sector of a circle?

The formula for the perimeter of a sector of a circle is:

\[
P = 2r + r\theta
\]

where:
- \( P \) is the perimeter of the sector.
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle of the sector in radians.

If the angle \( \theta \) is given in degrees, you must first convert it to radians using the formula:

\[
\theta \text{ (in radians)} = \theta \text{ (in degrees)} \times \frac{\pi}{180}
\]

The formula can also be expressed as:

\[
P = 2r + l
\]

where \( l = r\theta \) is the length of the arc of the sector.

Would you like more details on this or have any questions?

Here are some related questions you might find interesting:

1. What is the area of a sector of a circle?
2. How do you convert an angle from degrees to radians?
3. What is the formula for the circumference of a circle?
4. How do you calculate the arc length of a sector?
5. What is the perimeter of a semicircle?
6. How do you find the radius of a circle given the perimeter of a sector?
7. What is the difference between the perimeter of a sector and a segment?
8. How is the central angle of a sector related to the circumference?

**Tip:** Always remember that the perimeter of a sector includes both the arc length and the two radii that form the sector.

Explore the formula for the perimeter of a sector of a circle, including how to calculate it using radius and central angle. Learn the conversion of angles from degrees to radians. Suitable for Grades 10-12.

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