# The area of a sector

## Home learning focus

In this lesson you will understand what a sector is and learn how to find the area of a sector.

This lesson includes:

- learning summary
- one activity sheet

# Learn

Students looking to achieve grade 4 in GCSE Maths must understand how to calculate the area of a sector.

Read page 6 of our 'Circles, sectors and arcs' Bitesize revision guide to understand:

- what a sector is
- how to calculate the area of a sector

## What is a sector?

If you imagine a circle as a delicious pizza, a sector is a perfect slice running from the mid-point of the circle, with each cut a straight line - both the radius of the circle.

The two **radii** separate the area of a circle into two sectors - the **major sector** and the **minor sector.**

To work out the area of a sector, you need to use pi.

### What is pi?

The formula to work out the **area** for any circle is:

A = πr²

The symbol **π** is called **pi**.

The pi symbol (**π**) allows you to give the exact value to a calculation involving circles as pi cannot be written as an exact fraction or decimal. If a decimal answer is required, the value can be approximated as 3.14 (3 significant figures).

π = 3.14

Scientific calculators have a **π** button which can be used during calculations, with the final answer being rounded off as appropriate.

## Area of a sector

The formula to work out the area for any circle is:

Area of circle = πr².

The formula used to calculate the area of a sector of a circle is:

Area of a sector = Angle ÷ 360° × πr²

**Worked example**

Calculate the area of the sector shown (π = 3.14).

Using the equation: A = Angle ÷ 360° × πr²

144 ÷ 360 × 3.14 × 3² = 11.304

Rounding this figure to 2 decimal points gives the answer: 11.30 cm² as the area of the sector.

**Worked example**

Calculate the area of this sector which has a 60° angle, to one decimal place (π = 3.14).

60 ÷ 360 = 1/6 - 60° is one sixth of a full turn (360°), so the sector is ⅙ of the full area.

Use the equation: A = Angle ÷ 360° × πr²

The sector area is: ⅙ × 3.14 × 4² = 8.4 cm² (to 1 dp)

To learn more about sectors look at the Circles, sectors and arcs Bitesize guide here.

# Practise

## Activity 1

**Area of a sector**

Complete the activity sheet from White Rose Maths on finding the area of a sector to test your knowledge. You can print it out or write your answers on a piece of paper.

Click here to see the correct answers.

# Choose your exam specification

BBC Bitesize has GCSE exam board-relevant content for students in England, Northern Ireland and Wales. Chose the exam specification that matches the one you study.

# There's more to learn

Have a look at these other resources around the BBC and the web.