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In the figure below, ZAX is equilateral and has perimeter 30.

 

What is the exact area of the quadrilateral FLAX? Explain how you determined your answer.

 

https://ibb.co/ethVpx

hint: FLAX is not a square!

sageatron2000  Apr 10, 2018
edited by sageatron2000  Apr 10, 2018
 #1
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If ZAX  is equilateral  and has a perimeter of 30, then  XA  must  = 10

 

So...ZA  must also  = 10

 

Note that angle ZAX  = 60...so angle LAZ  = 90 - 60  = 30

 

And we can find LA   thusly :

 

cos LAZ   = LA / ZA

 

cos (30)  = LA / 10

 

10 cos (30 )  = LA

 

10 √3/2  = LA   =  5√3

 

So....the area of FLAX  =    XA  *  LA   =   10 * 5√3   =  50√3  units^2  

 

 

cool cool cool  

CPhill  Apr 10, 2018

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