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If the perimeter and radius of a sector are 38 and 9 cm respectively . find its area.

 

 Jul 2, 2020
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The perimeter  is given by :

 

2* radius  + arc lengrh of the  sector  =

 

2r   +  r* theta      where  theta  is the measure  of the central  angle of the sector ( in radians)

 

So   we  have  that

 

38  =  2r  + r * theta     simplify

 

38 = r ( 2 + theta)    subbing   in for the radius  we  have that

 

38 = 9 (2 + theta)    divide both sides by  9

 

(38/9)  = 2 + theta     subtract 2 from both sides

 

20/9 =  theta  

 

The area of  the sector =   (1/2)* r^2 * theta

 

So....the area  =    (1/2) (9)^2  * ( 20/9)  =   (1/2) ( 9) (20)  =   90 cm^2

 

 

cool cool cool

 Jul 2, 2020

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