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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

#1**+2 **

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

CPhill Nov 30, 2017