the assumption being that GLEB is a plane to the brown rectangular prism.
I'm afraid the question is either missing information or simply very misleading.
GLEB is perpendicular to what? the assumption here being perpendicular to the base of the prism.
now, if the plane GLEB lies perpendicular to the base of the prism, yet none of sides are parallel to any of the sides of the prism, will the cross-section be a rectangle? well, a rectangle requires 90° angles, and if the prism has all 90° angles at its corners, any perpendicular cross-section that doesn't parallelize with its sides does not make a rectangle.
