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Sector help. How to find the area of a sector using A = x/360 × π × r²

Updated on March 28, 2013

Area Of A Sector Video

To find the area of a sector using a calculator you can substitute your numbers into the following formula:

A = x/360 × π × r²

Key:

A is the area of the sector.

x is the angle of the sector.

r is the radius of the sector.

All you need to do is substitute your numbers into your formula correctly and type in what you have written down on your calculator. The fraction button can be used on your calculator to make things easier.

Also notice that the only difference between the formula for the area of a sector and the area of a circle is that x/360 comes before π × r². This gives you the required proportion of the circle.

Let’s take a look at a couple of examples on finding the area of a sector.

Example 1

Find the area of this sector.

First write down your formula down for finding the area of the sector:

A = x/360 × π × r²

Now the radius of the circle is 7cm and the angle of the sector is 67⁰.

So substitute these numbers into the formula above.

A= 67/360 × π × 7²

You can type this all in one go on your calculator if you use the fraction button.

A= 28.6 cm² to 3 significant figures.

Example 2

Another sector has a radius of 5 m and an inside angle of 275⁰. Work out the area of the sector.

Begin by writing down the formula for the area of the sector.

A = x/360 × π × r²

Now the radius of the circle is 5 m and the angle of the sector is 275⁰.

So substitute these numbers into the formula above.

A = 275/360 × π × 5²

Again type this exactly as above on your calculator to give the final answer.

A= 60.0 m² to 3 significant figures.

For some more worked questions on finding the area of a sectors click here.

For some real life examples on working out the area of a sector click here.

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    pholoso sibanda 4 years ago

    thanks a lot with a lot with those simple and straight example.