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

#1**+1 **

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

CPhill
Apr 10, 2018