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In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $150^\circ.$  Find the area of the rhombus.

 Dec 31, 2023

Best Answer 

 #1
avatar+676 
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In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $150^\circ.$  Find the area of the rhombus.     

 

                             Area  =  base • height    

 

                             Area  =  12 • 6  

 

                             Area  =  72  

 

Where did that value for the height come from?  

 

One of the angles is 150o so the one next to it is 30o.  

 

Drop a perpendicular from the 150o angle at the top vertex.   

Use trig.  You know the hypotenuse is 12 and the angle is 30o.  

 

sin(30) = h / 12   (opposite over hypotenuse)  

0.5 = h / 12   ====>  h = 6  

.

 Jan 1, 2024
 #1
avatar+676 
+1
Best Answer

 

In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $150^\circ.$  Find the area of the rhombus.     

 

                             Area  =  base • height    

 

                             Area  =  12 • 6  

 

                             Area  =  72  

 

Where did that value for the height come from?  

 

One of the angles is 150o so the one next to it is 30o.  

 

Drop a perpendicular from the 150o angle at the top vertex.   

Use trig.  You know the hypotenuse is 12 and the angle is 30o.  

 

sin(30) = h / 12   (opposite over hypotenuse)  

0.5 = h / 12   ====>  h = 6  

.

Bosco Jan 1, 2024

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