A regular hexagon is circumscribed about a the ring surrounding the clock face. The diameter of the ring is...

The diameter of the ring is 10in. Find the perimeter of the hexagon. PLEASE HELP. Geometry homework help! The answer is 34.6in but i don't know how to get to that answer and I have to show my work.

You mean I have to show my work, and then you can copy it (without crediting me)...right?

The diameter of the circle is 10, so the radius is 5
A regular hexagon can be divided into 6 equal equilateral triangles.
Each one of these equilateral triangles has a height of 5 inches.

Now, with a little help from the Pythagorean Theorem, we can figure out what each side of the hexagon measures

(L/2)^2 + 5^2 = L^2
L^2 / 4 + 25 = L^2
L^2 + 100 = 4L^2
100 = 3L^2
10 = sqrt(3) * L
10 / sqrt(3) = L

Each side is 10 / sqrt(3) inches. Multiply that by 6 (the number of sides for the hexagon)

6 * 10 / sqrt(3) =>
60 / sqrt(3) =>
60 * sqrt(3) / 3 =>
20 * sqrt(3) =>
20 * 1.732 (roughly) =>
17.32 * 2 =>
34.64

34.6 inches, roughly.

EDIT:

An equilateral triangle is an isosceles triangle
All isosceles triangles can be made from 2 identical right triangles
In this case, each right triangle is a 30-60-90 triangle
All 30-60-90 triangles have the following property: the shortest side is half the hypotenuse
The rest is just the pythagorean theorem