Determining Hexagon Dimensions

[ImpShial]

Does anyone know if there is a way to get precise dimensions of a hexagon by starting with the distance between flat sides?

Example:


Say the distance between the top and bottom is 1.5 inches. How would I go about determining the dimensions of the rest of the hex?

I don't know a lot of math, so please explain in lay terms if possible. I'm trying to learn all I can about hexagons and determing dimensions.

Thank You,

Imp

[kedaman]

it should follow that the hexagon is regular if the distance between each opposite side is the same as the given. In an n-gon the sum of angles is (n-2)*180 degrees so for a hexagon the sum is 720 degrees, and a regular hexagon all angles are the same, 720/6 degrees=120 degrees. If we cut the hexagon from each corner to opposite corner, they will cut them in two, so each angle in the cut slices two outher corners are 60 degrees, and the inner corner is (3-2)*180-2*60 degrees=60 degrees. These slices are all all regular triangles of the same size with the height half of the distance between the opposite sides of the hexagon and the base is height/sin30, thus the area is 6*(distance/2)^2/sqrt3

[fundu]

If the hexagon is regular that is all the sides are equal and the distance between the two opposite sides is d (assume), then

the length of any side will be d/sqrt(3)

The rest of the things can be then calculated as required