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In the figure below, angle Z A X is equilateral and has perimeter 30.

What is the exact area of the quadrilateral F L A X?

 

Guest Nov 30, 2017
edited by Guest  Nov 30, 2017
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If ZAX is equilateral and has a perimeter of 30, then each side must  = 10

 

And...due to symmetry, ZL is (1/2)XA

 

And XA  =  10...so  ZL   = 5

 

So triangle ZLA is a right triangle...so using the Pythagorean Theorem :

 

LA  =  √ [ ZA^2   - ZL^2 ]

 

LA  = √ [ 10^2  - 5^2 ] 

 

LA  =  √ [100 - 25 ] =  √ 75  =  √25 *√ 3   =  5√3

 

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

 

 

cool cool cool

CPhill  Nov 30, 2017
edited by CPhill  Nov 30, 2017

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