# How can I determine the sides in a squished hexagon?

How can I determine the sides, and the angle with horizontal, in a squished hexagon ?

(coordinates (75,0); (25,0); (0, 50*sin60);(25,100*sin60); (75,100*sin60); (100,50*sin60)
to fit in a smallest rectangle size (w0=100, h0=100*sin60)) - see first picture,
then I resize it to a box of new size (w,h)

How can I determine the new sides of the hexagon, and the angle theta, based on the new sizes w and h ?

I started trying some type of equation, based on right triangle trigonometry, but it got very complicated - even with my initial assumption that the oblique sides will be equal to the horizontal ones, which I see in my picture that they don't seem to be equal...

Is the problem possible, and do I have enough information ?

I really need the size of the oblique sides and/or the angle they make with the horizontal (knowing one would give me the other).

I hope someone can give me a solution...

I tried to figure it out but it seems incorrect.