Question

Pls help!! Thank you sooooo much if you help me on this, pls show proof

Answer 1

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