A square.
No, a cube cannot have an octagonal cross-section.
Rectangle
The cross section of a pyramid shrinks from the shape of the base down to a point as you move along its axis from the base to the apex. The cross section of a prism is constant along its axis.
It is a triangle.
No because it would be smaller.
No, a cube cannot have an octagonal cross-section.
The cross-section of a cube can vary depending on how it is cut. If sliced parallel to one of its faces, the cross-section will be a square. If cut diagonally, the cross-section can be a rectangle or a more complex polygon, depending on the angle and position of the cut.
A square
The cross sectional area of a triangular prism is simply the area of the base. The formula for the area of a triangle in one half base times height. Remember that a triangular prism by definition has a triangle for a base.
Yes it can.
Infinitely many.
Rectangle
A cross section of a cube is formed by slicing through it in various ways. Shapes that cannot be a cross section of a cube include those with curved edges, such as circles or ellipses, as well as shapes with more than six sides, like an octagon. Additionally, any shape that cannot be formed by connecting straight lines or does not lie flat, such as a 3D object, would also not be a valid cross section of a cube.
Yes, but not a regular one.
It will be the same shape as a square
A cylinder has a circular cross section that is parallel to its base.
The cross section of a pyramid shrinks from the shape of the base down to a point as you move along its axis from the base to the apex. The cross section of a prism is constant along its axis.