Find the number of units in the length of diagonal DA of the regular hexagon shown. Express your answer in simplest radical form.

For a polygon, the SUM of the internal angles is  (n-2) * 180    (n=6 for hexagon)

(6-2)*180 = 720     Thus EACH angle is :   720/6 = 120 degrees

So the large angle of the triangle is 120 degrees    the other two are equal to each other

  there are 180 degrees in any triangle:   

   (180-120) / 2 = 30 degrees for each of the smaller angles.

Now use the law of sines

10/sin30 = x/(sin120)

10/(.5)  * (sqrt3 )/ 2 = x

10 sqrt 3

10/sin30  *  sin 120  =  17.32

I already drew a diagram, but don't know how to upload it from my computer.

First you connect the point A to the two points that construct the line segment labeled 10. 

AD is congruent to the line segment perpendicular to the side labelled 10. 

You have constructed a 30 - 60 - 90 triangle. The hypotenuse is 20.

The leg is the square root of 20^2 - 10^2.

Can someone tell me how to upload an image, then this solution would be much clearer. 

Thanks

As an alternative,  we can use the Law of Cosines to solve this

The interior angle of a hexagon = 120°....so....

AD^2  = 10^2 + 10^2  - 2 (10 *10) cos (120°)

AD^2  = 200  - 200 (- 1 / 2)

AD^2  =  200 + 100

AD = √ [300]  ≈  17.32  units