Geometry Help?

Question

If a hexagon has a radius (center to point of angle) of 6, what is the side of the hexagon?

Answer 1

Draw two radius lines with name x, y to form a triangle with one of the side of the hexagon.

Now the angle between x and y is 60 degrees ( 360 / 6)

So the side of the Hexagon (z) = x * y * Sine 60

So its = 36 * Sine 60

Answer 2

hexagon has 6 sides.... and if the radiu from the center to a corner is 6 you have an isoceles triangle....
from the center is 360 degress...

360 / 6 = 60

but since the angle the radii make is 60 and you have 2 equal side the remainder of the angles = 120 degrees because the sum of the angels in a triangle = 180.

in an isoceles triangle the 2 base angle equal each other...

120 / 2 = 60

now your 3 angles are all 60 degrees and since all the angles are the same all the sides will be the same which creates an equalateral triangle.... each side of the hexagon equals the length of the radiu the length of each side is 6 and has a perimeter of 36

so answering your question each side of the hexagon is 6

Answer 3

In a regular hexagon, 6 triangles are equilateral triangles
Each side subtends an angle of 360/6 = 60 and other two angles are equal > (180 - 60)/2 = 60 deg each
So the radius and each side are equal
side = 6

Answer 4

I assume you are talking about a "regular hexagon", all sides and angles are equal.

In this case, all internal angles of the hexagon are 120°. When you draw the radius, you bisect this angle, giving you two angles of 60° each.

If you draw another radius to a neighboring point, you have now created an equilateral triangle. Since it is equilateral (all sides are equal), the sides of the hexagon are also 6.

Answer 5

x = 2 * 6sin30 = 6