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Find the Area of a Sector

In this worksheet, students will learn the formula for finding the area of a sector and be able to apply it.

'Find the Area of a Sector ' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Area Calculations

Popular topics:   Area worksheets

Difficulty level:  

Worksheet Overview

When you go to a pizza restaurant, you're probably too hungry to be wondering where the maths is, aren't you?




Take this humble pizza, where is the maths in that?

The slice you have just cut for yourself is called a sector.


A sector is the area between an arc of a circle and its two radii.

So to find out how much you have cut, you would need to find the area of the sector.


As ever, there is a formula to do this.

As we are looking at part of a circle,  is involved of course.


To find the area of a circle we use the formula πr² or (π x r x r)


It makes sense to use this to find the sector.

Remember that you can use the π button on your calculator or use the value 3.14


Area of a sector =  angle ÷ 360 x π x radius x radius   or   (angle ÷ 360 x πr²)


Let's calculate how hungry you are!




The radius of the pizza is 6 cm and the angle is 50°

50 ÷ 360 x π x 6 x 6 = 15.71 cm²


To save a lot of writing down in mid calculation, it is best if you use a scientific calculator as you can put the whole formula in at once.

The calculator is clever enough to know the value of pi too.


Let's move on to some questions now.

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