Projected area, is maple able to compute?

If I was to project a squared profile onto a cylinder. Would mable be able to help me calculating the area that is projected onto the cylinder?

Since the cylinder walls are curved I assume that the are projected on to the curved surface which is the wass of the cylinder is bigger then side*side.

In the link I tried to sketch the "problem" the red square represent the area I want to project onto the cylinder.

https://i.gyazo.com/4113ad5255385b438c8872941e14baf1.png

Thanks