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please help me with this one

melvsky  May 2, 2018
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 #1
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Note....that the diagonals of a rhombus are perpendicular.....they  form  a  90 degree angle

 

So...triangle  CEB  is a 30-60-90 right triangle

 

The hypotenuse of this triangle is 12

Angle ECB  = 30 degrees.....and the side opposite this angle   = 1/2 of the hypotenuse  =  6

So EB  = 6......and since the diagonals bisect each other....then  DB  = 12

 

Also..in triangle CEB....the side opposite the 60 degree angle  = √3  times the side  opposite the 30 degree angle  = 6√3

So.....CE  =  6√3    and CA  = 2 * 6√3  =  12√3

 

So...the area  =  (1/2) product of the diagonal lengths  =

 

(1/2) (12) (12√3)  =

 

72√3   units^2

 

 

 

 

cool cool cool

CPhill  May 2, 2018
 #2
avatar+51 
+1

Thank you so much! You reinforced some of my learned concepts and really helped me complete/understand my homework! laugh

melvsky  May 2, 2018

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