1. Arc length
and
area of a sector

2. Arc Length
An arc of a circle is a portion of the circumference formed by a central angle. It’s the length of the pie crust! θ

3. Arc Length
The arc length s of a circle radius r, subtended by a central angle of θ radians, is given by:
s = rθ
The angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

4. “Subtended?” That just means “formed by.”
Example 1: Arc Length
Find the length of the arc of a circle of radius 4 meters subtended by a central angle of 0.5 radian.
“Subtended?” That just means “formed by.”

5. Area of a Sector
A sector of a circle is a portion of the circle formed by a central angle. It’s the area of a slice of pie! θ

6. Area of a Sector
The area of a sector A of a circle radius r, subtended by a central angle of θ radians, is given by:
A = ½r2θ
Again, the angle must ALWAYS BE IN RADIANS. Sometimes it will be given in degrees to trick you. Convert it to radians!

7. Example 2: Area of a Sector
Find the area of the sector of a circle of radius 5 feet subtended by an angle of 60°. Round the answer to two decimal places.
“Subtended?” That just means “formed by.”

8. Put it all together!
Arc Length Area of a Sector s = rθ A = ½r2θ Length of pie crust Area of a slice