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

## 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.

## More by this Author

- 0
The density, mass and volume triangle is as follows: So if you wanted to work out the density, you would cover up density in the magic triangle to give: Density = Mass/Volume (since mass is above volume) So if...

- 14
Finding the nth term of a decreasing linear sequence can by harder to do than increasing sequences, as you have to be confident with your negative numbers. A decreasing linear sequence is a sequence that goes down...

- 0
The surface area of a triangular prism can be found in the same way as any other type of prism. All you need to do is calculate the total area of all of the faces. A triangular prism has 5 faces, 3 being rectangular and...