The figure below shows a right rectangular prism whose base is a 2x2 square and whose height is 4.Which shape does the intersection of the vertical plane with the prism look like?

Answer: To determine the shape of the intersection of a vertical plane with the right rectangular prism, we need to consider the orientation of the plane relative to the prism. However, since the base of the prism is a 2x2 square and the height is 4, if the vertical plane cuts through the prism parallel to one of its faces, the intersection would be a rectangle.

The reason for this is that a vertical plane parallel to the side faces (which are rectangles) would cut a 2x4 rectangle out of each of these faces. If the plane is parallel to the front and back faces of the prism, then it would cut out 2x2 squares, since these are the dimensions of the base. If the question assumes that the vertical plane cuts through in any other non-parallel manner, then the intersection could be a variety of quadrilaterals, depending on the angle and position of the cut.

Extra: A right rectangular prism is a three-dimensional solid with six rectangular faces where each angle is a right angle (90 degrees). If a vertical plane (a plane that stands upright) intersects the prism, the resulting cross-section will be a two-dimensional shape. The plane can cut the prism in many ways, and the shape of the intersection will depend on the orientation of that plane.

Possible intersection shapes based on different plane orientations could be:

1. Rectangle: If the plane cuts parallel to any of the rectangular faces of the prism (most common scenario). 2. Triangle: If the plane cuts through one of the side faces and the top or bottom at an angle. 3. Quadrilateral: If the plane cuts the prism at some other oblique angle — not parallel to any face — the result could be a general quadrilateral.

For students learning geometry, this can be a practical exercise in visualizing how two- and three-dimensional geometrical shapes interact. By understanding the properties of these basic shapes, students can predict the outcome of these intersections which can be useful in various real-world applications, such as engineering and architecture.