Sector Area
Part of the circle’s area.
Key idea
Part of the circle’s area.
In depth
A sector is a pie slice. Its area is the same fraction of the whole circle as its angle is of 360°: A = (θ/360) × πr². In radians, A = ½r²θ.
Worked example
A 90° sector of radius 4: (1/4) × π × 16 = 4π ≈ 12.57.
Formula
Real-world uses
- Calculating the size of a slice of pie or a sprinkler’s watered area
Common mistake
Confusing sector area with arc length.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Sector Area?
Part of the circle’s area. It is a topic at the advanced level in Geometry.
What is the formula for Sector Area?
The key formula is A = ½ r² θ.
Where is Sector Area used in real life?
Real-world examples: Calculating the size of a slice of pie or a sprinkler’s watered area.
What should I learn before Sector Area?
Make sure you are comfortable with Arc Length of a Circle, the previous topic in Geometry.
What is a common mistake with Sector Area?
Confusing sector area with arc length.
How can I practise Sector Area?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Sector Area?
Move on to Central and Inscribed Angles next.
Related advanced topics in Geometry
- Heron’s Formula – Triangle area from three sides.
- Regular Polygon Area – Use apothem and perimeter.
- Arc Length of a Circle – Part of the circumference.
- Central and Inscribed Angles – An inscribed angle is half the central angle on the same arc.
- Chord and Tangent Properties – A tangent is perpendicular to the radius at the point of contact.
- Cones – Volume and surface area of a cone.