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Perimeter of a Sector

Perimeter of a sector_1


As we saw in parts of a circle, a sector is the area bounded by an arc and two radii. It looks like a piece of pizza or a piece of a pie.



Perimeter of a sector_2


Perimeter of a sector consists of the two radii and a curved section, which is the arc of the circle.


We first need to find the length, l of the arc. It is given by the equation

l  =  theta/360~*~2 pi r

In other words, l is theta/360 of the circumference of the circle, which will give us the length of the arc.

Perimeter of the sector is then the sum of the two radii and the length of the arc.

Perimeter  =  r + r  + l

=  2r + theta/360~*~2 pi r


Example 1 : Calculate the perimeter of the sector shown, correct to 1 decimal place.

Perimeter of the sector  =  2 times radius plus arc length  Perimeter of a sector_example1

=  2r  +  theta/360~*~2 pi r

=  2 x 4  +  60/360x 2 x 3.14 x 4

=  8 + 4.2

=  12.2 mm (to 1 decimal place)


Example 2 : What is the perimeter of the quadrant with radius 7.2 cm?

Perimeter  =  2r + theta/360~*~2pi r  Perimeter of a sector_example2

=  2 x 7.2 + 90/360x 2 x 3.14 x 7.2

=  14.4 + 11.3

=  25.7 cm (to 1 decimal place)


Here are a few more examples of perimeter of a sector.