Answer:
√468 = 6√13
Step-by-step explanation:
ABCDEF is a regular hexagon of side length 6.
A'B'C'D'E'F' is the reflection of ABCDEF across BC.
The line FE' is the line from F to E'. It is also the hypotenuse of the right triangle FEE'. FE = 6, and EE' = 4a, where a is the apothem of the hexagon.
To find the apothem, draw the 30-60-90 triangle formed by the apothem and the radius (essentially 1/12th of the hexagon).
Using properties of a 30-60-90 triangle:
a = (6/2)√3
a = 3√3
4a = 12√3
Using Pythagorean theorem:
x² = (6)² + (12√3)²
x² = 36 + 432
x = √468
x = 6√13
