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In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.

 Mar 27, 2024
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In a rhombus, all the side lengths are $12,$ and one of the angles is equal to $20^\circ.$ Find the area of the rhombus.   

 

Visualize, or preferably draw, the rhombus, leaning sharply to the right.  

 

Drop a perpendicular from the upper left vertex to the bottom side. 

 

This has made a right triangle with a 20o angle and the hypotenuse 12.  

 

Use trig to find that height..       sin(20o)  =  height / 12  

 

                                                    0.3420  =  height / 12 

 

                                                      height  =  0.3420 • 12  =  4.104

 

                                            Arearhombus  =  base • height 

 

                                                        Area  =  12 • 4.104 

 

                                                        Area  =  49.25  

 

Note that I rounded the decimal values that I wrote down.    

If you calculate it using those values, you'll get 49.248.   

I calculated it without rounding, that's where I got 49.25.  

.

 Mar 28, 2024

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