As a former HS math teacher, I often want to give Rhino very bad grades… What am i doing wrong?

Here are two Simple bent piece of material. I want to develop them into a flat surface To be able to have then wirecut… In blue are the parts.

I drew an extrusion that follow the 1/2 thickness profile to find the median plane( in Black.

So mathematically from my 5th grade math class, what I am looking for is the intersection of the blue part with the black extrusion. As result I am expecting a surface that has the contour of the blue part… Well not according to Rhino.

FIrst Part what I selected:

the result:

Since when the intersection of a volume with a surface is a volume? 0/10

Now for the second set:

First and second surfaces selected:

Result:

Another solid 0/20…

OK I can now explode the resulting object and keep the faces I need but why the extra work…