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In parallelogram ABCD, AB=125cm, AD=132cm, and the length of diagonal AC is 32cm. The area of the parallelogram, in cm2, is

 
 Jun 4, 2021
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Since we  have a parallelogram.....

 

AB  =   DC  =   125

 

We can  find  the cosine  of angle  ADC    with the Law of Cosines

 

AC^2  =  AD^2  +  DC^2  cos ( ADC)

 

32^2  =  132^2  +  125^2   -  2 ( 132 * 125)  cos (ADC)

 

[ 32^2  - 132^2  - 125^2 ]  / [ -2 * 132  * 125 ]  = cos ADC  =  427/440

 

sin ADC  =   sqrt  [ 1 - (427/440)^2 ]    =     (17/440)sqrt (39)

 

The  area  is

 

AD  *  DC   sin  ADC   =  

 

132  * 125  *  ( 17/440) sqrt(39)    ≈   3981.19  cm^2

 

 

cool cool cool

 
 Jun 4, 2021
edited by CPhill  Jun 4, 2021
edited by CPhill  Jun 4, 2021

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