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Examples of Area of a Sector

Here are a few more examples of area of a sector. Calculate the area of the following sectors, correct to 1 decimal place.

 

Example 1 : Area of a sector  =  theta/360~*~pir2  Examples of area of a sector_1

=  180/360 x 3.14 x 122   (since r = 12 mm)

=  226.1 mm2 (to 1 decimal place)

 

Example 2 : Area of a sector  =  theta/360~*~pir2  Examples of area of a sector_2

=  15/360 x 3.14 x 272   (since r = 27 mm)

=  95.4 cm2 (to 1 decimal place)

 

Example 3 : Area of a sector  =  theta/360~*~pir2  Examples of area of a sector_3

=  140/360 x 3.14 x 172   (since r = 17 m)

=  352.9 m2 (to 1 decimal place)

 

Example 4 : Area of a sector  =  theta/360~*~pir2 Examples of area of a sector_4

=  222/360 x 3.14 x 322   (since r = 32 mm)

=  1982.8 mm2 (to 1 decimal place)

 

Example 5 : Area of a sector  =  theta/360~*~pir2  Examples of area of a sector_5

=  45/360 x 3.14 x 92   (since r = 9 m)

=  31.8 m2 (to 1 decimal place)

 

Example 6 : Calculate the area of the figure shown below, correct to one decimal place.

We need to find the area of the sector but the given angle is outside the sector. Hence we need to find the angle inside the sector.  Examples of area of a sector_6

So the angle covering the arc  =  360° – 55°  =  305°

Area of a sector  =  theta/360~*~pir2

=  305/360 x 3.14 x 182 (since r = 18 cm)

=  861.9 cm2 (to 1 decimal place)

 

Here are some extension problems in area of a sector