Area of a circle (AQA GCSE Maths): Revision Notes

Area of a circle

The formula you need to know

The formula for calculating the area of a circle is one of the most fundamental concepts in geometry. Understanding this formula and knowing how to apply it correctly is essential for success in mathematics.

$\text{Area of a circle} = \pi \times \text{radius}^2$

This can also be written as $A = \pi r^2$

Converting diameter to radius

When working with circles, questions might give you different measurements. If a question provides the diameter, you must convert it to radius before calculating the area.

$\text{Diameter} \div 2 = \text{radius}$

Step-by-step method for calculating area

Following a systematic approach ensures accuracy and helps you avoid common errors. Here's the recommended method for calculating the area of any circle:

1. Identify the radius - if you're given the diameter, divide by 2
2. Square the radius - multiply it by itself
3. Multiply by π - use the π button on your calculator
4. Round your answer appropriately and include units (usually cm²)

Working with semicircles

A semicircle is exactly half of a complete circle, which means we need to modify our area formula accordingly. This concept appears frequently in geometry problems and compound shape calculations.

$\text{Area of semicircle} = \frac{1}{2} \times \pi \times \text{radius}^2$

Compound area calculations

When finding shaded areas involving semicircles, you often need to calculate multiple areas and then combine them using addition or subtraction.

Key exam tips

Success in circle area problems comes from understanding the concepts and avoiding common pitfalls. Here are the most important strategies to remember:

Show your working clearly

Check what you're given

Use appropriate rounding

Practice opportunity