Area of a Circle
Area is π times radius squared.
Key idea
Area is π times radius squared.
In depth
A = πr². Slice a circle into thin wedges and rearrange them into a near-rectangle with width πr (half the circumference) and height r, giving area πr × r.
Worked example
Radius 3: A = π × 9 ≈ 28.27.
Formula
Real-world uses
- Working out how much turf a round lawn needs
- The cross-sectional area of a pipe
Common mistake
Writing A = (πr)². The radius is squared, not π.
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 Area of a Circle?
Area is π times radius squared. It is a topic at the intermediate level in Geometry.
What is the formula for Area of a Circle?
The key formula is A = πr².
Where is Area of a Circle used in real life?
Real-world examples: Working out how much turf a round lawn needs; The cross-sectional area of a pipe.
What should I learn before Area of a Circle?
Make sure you are comfortable with Circumference, the previous topic in Geometry.
What is a common mistake with Area of a Circle?
Writing A = (πr)². The radius is squared, not π.
How can I practise Area of a Circle?
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 Area of a Circle?
Move on to The Number Pi next.
Related intermediate topics in Geometry
- Vertical Angles – Opposite angles formed by intersecting lines are equal.
- Parallel Lines and Transversals – Corresponding and alternate interior angles are equal.
- Exterior Angle Theorem – An exterior angle equals the sum of the two remote interior angles.
- Triangle Inequality – Any two sides sum to more than the third.
- Congruent Triangles – Same shape and size: SSS, SAS, ASA, AAS, HL.
- Similar Triangles – Same shape, proportional sides: AA, SAS~, SSS~.