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A chord of length 6 units divides a circle into two distinct areas. If the circle has a radius of 6 units, what is the area of the larger region, in square units? Express your answer in simplest radical form in terms of \(\pi\)  .

tertre  May 19, 2017
 #1
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The smaller area between the chord and the edge of the circle is given  by :

 

(1/2)*6^2 (pi/3)- (1/2)*6^2 sin (60)  =  36 ( pi/3 - √3/2)  (1)

 

The area  of the whole circle  =  pi (6^2)  =  36pi     (2)

 

So  the area  of the  larger part   =  (2)  - (1)  =

 

36pi  - 36 ( pi/3 - √3/2)  =

 

36   [  pi  - pi/3 + √3/2 ]  =

 

36 [ 2pi / 3  + √3/2]  =

 

[ 24pi + 18√3 ]  units^2 

 

 

cool cool cool

CPhill  May 19, 2017

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