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# Area of a 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.

There 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

a 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  =  r2

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

Area  =  r2

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

Area  =  r2

=  42

=  x 3.14 x 16

=  4.2 m2  (to 1 decimal place)

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

A  =   r2

=  x 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.