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?
+130099 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
