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
Revise - sectors

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.

Area of a sector

Click here to see the correct answers.

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