Regular hexagon ABCDEF has side length 1.

Regular hexagon ABCDEF has side length 1.
Give the length of diagonal AE.
A. √2
B.
C. √3
D.
E.

Correct Answer: C
Explanation/Reference:
Explanation:
The key is to examine ΔAED in the figure below:

Each interior angle of a regular hexagon, including angle F, measures 120°, so it can be easily deduced by way of the Isosceles Triangle Theorem that

To find

we subtract

Thus resullting in
Also, by symmetry,


and ΔAED is a 30°-60°-90° triangle whose short leg ED has length ED = 1.
The long leg AE of this 30°-60°-90° triangle measures √3 times the length of short leg ED so AE = √3.

Download Printable PDF. VALID exam to help you PASS.