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Area of a Sector

Area of a sector_minor sector

 

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 pie.

 

Area of a sector_quadrantThere are two special types of sectors, viz.,

a quadrant or a quarter circle – it is bound by two radii that are at right angles to each other, and

 

Area of a sector_semicirclea semi-circle or half circle. It is bound by the two radii that form a straight line (or 180°)

 

 

The formula for area of a circle is  A  =  pir2

Since a sector only represents part of a circle – specified by the angle theta between the two radii – the area of a sector is given by:

Area  =  theta/360~*~pir2

 

Example 1 : What is the area of the sector with radius 4m and theta = 30°

Area  =  theta/360~*~pi~*r2 Area of a sector_example1

=  30/360~*~pi~*42

=  1/12x 3.14 x 16

=  4.2 m2  (to 1 decimal place)

 

Example 2 : What is the area of the semi-circle?

A  =  theta/360~*~pi~* r2  Area of a sector_example2

=  180/360x 3.14 x 62  (since r = 12/2 = 6 mm)

=  56.5 mm2  (correct to 1 decimal place)

 

Here are a few more examples of area of a sector, and some extension problems in area of a sector.