Lesson video

Hello, my name is Miss Parnham.

In this lesson, we're going to learn how to find the area of a sector.

Let's look at an example of how to find the area of a sector.

In this example, the angle of the sector is 240 degrees.

This is two thirds of a circle because 120 degrees is a third of 360 and double 120 is 240.

So we will start this question by first working out the area of the complete circle with the radius 15 metres.

So we do that by using the formula of Pi r squared.

That gives us 225 Pi, which is 707 metres squared when rounded to three significant figures.

We're going to calculate with this now.

And therefore we would leave, the full answer in our calculator to get accuracy.

So let's divide this by three in order to find out the area of a sector with angle 120 degrees, you know the words, a third of a circle.

So that gives us 75 Pi or 236 metres squared to three significant figures.

Again, leave this number in your calculator so that we can get an accurate answer when we calculate with it.

This is now going to be doubled because we are looking for an angle of 240 degrees, which is double 120 degrees or two thirds rather than one third.

So multiplying that by two gives us 150 Pi, which is equivalent to 471 metre squared to three significant figures.

Here is a question for you to try.

pause the video, to complete the task and restart the video when you're finished.

Here are the answers.

Did you notice that the third sector was two thirds the area of a full circle? And the fifth sector was three quarters the area of a complete circle.

Here's some questions for you to try.

Pause the video, to complete the task and restart the video when you're finished.

Here are the answers.

Hopefully the previous question helped you to find these areas quickly as they are all familiar fractions of a complete circle.

So Pi was a sixth of a full circle, B a third, C two thirds and D three quarters.

Here's a further question for you to try.

Pause the video to complete the task and restart the video when you've finished.

Here are the answers.

Did you notice that in part C you were given the angle outside the sector.

So you needed to subtract 120 from 360 day to find 240.

As in the previous question, these sectors were all familiar fractions of a complete circle.

Now let's look at an example with a sector, which has an angle, which is not a familiar fraction of 360.

In the same way as before, let's work out the area of a circle with the same radius which is 12.

6 centimetre squared.

So we square that radius.

We multiply it by Pi and the answer to three significant figures is 499.

Remember to leave that full accurate answer on your calculator because we're going to need that to work out the area of this sector.

So all we do is find the fraction using the angle that we're given for the sector over 360.

And then we can multiply that fraction by the area of the full circle to find the area of the sector.

So we take the 499 and multiply it by 234 over 360.

If you prefer, you could multiply by 234 and then divide by 360, or you could divide by 360 and then multiply by 234.

All three methods get you to the same answer.

The final answer of 324 centimetres squared to three significant figures is the area of this sector.

Here's a question for you to try.

Pause the video to complete the task and restart the video when you're finished.

Here are the answers.

Always remember that you begin with a radius perhaps given in millimetres centimetres or metres.

It's a measurement of distance, But your answers are area and need to be given as millimetres squared, centimetres squared or metres squared.

That's all for this lesson.

Thank you for watching.