Question

Describe the shape resulting from a vertical, angled, and , horizontal cross section of a rectangular prism.

Answer 1

For example, lets say:
L = 10
H = 6
W = 4

Imagine the shape is facing slightly towards your left
A left vertical cross section (perpendicular to the base) of the cuboid would result in a 10 by 6 rectangle
A right vertical cross section (perpendicular to the base) of the cuboid would result in a 6 by 4 rectangle
A horizontal cross section (parallel to the base) of the cuboid would result in a 10 by 4 rectangle
An angled cross section (through the middle) would also give a rectangle but the dimensions would be different. If the cut went from one '4' edge to the one in the opposite corner, the length of that would be found using Pythagoras
a² + b² = c²
6² + 10² = c²
36 + 100 = 136
√136 ≈ 11.66cm
11.66 by 4 rectangle

The shows that the resulting shape will always be a rectangle for these cross sections.
The only case in which it would not, would be if one of the faces of the cuboid was a square - in which case one of the cross sections would also be a square.