Rotation of a square on a plane

Hi All,

I hope you can help (and I hope this is the right forum for this subject)

I have a resizeable plane (say 300 x 300 in size)

On this plane I have a square (say 290 x 290 in size)

When i rotate this square on this plane by say 25 degrees around the squares center parts of the square are no longer visible on the existing plane.

My goal is to have the plane resize based on the new square but all I have available is the original dimensions of the plane, the original dimensions of the square and the angle it's being rotated by in my problem i do have access to various trigonometric functions such as cos and sin, I also know the center of the original square.

basically i'm looking for an equation which would take the angle and dimensions of the original square and plane and produce the new correct dimensions for the plane so that it engulfs the new square

Please anyone that could help I am desperate for help

kind regards

James