rhombus

 

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 150^o so the one next to it is 30^o.  

 

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

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

 

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

0.5 = h / 12   ====>  h = 6  

^.