All the Cross-Sections of a Rectangular Prism

The cross-sections of a rectangular prism are the two-dimensional figures that are obtained when we cut a prism with a plane. The figure formed depends on the orientation of the plane. We can obtain rectangular, triangular, pentagonal, and hexagonal cross-sections.

Here, we will learn about the cross-sections of a rectangular prism in detail using diagrams.

GEOMETRY
cross section of a rectangular prism

Relevant for

Learning about all the cross-sections of a rectangular prism.

See cross-sections

GEOMETRY
cross section of a rectangular prism

Relevant for

Learning about all the cross-sections of a rectangular prism.

See cross-sections

Rectangular cross-section

The rectangular cross-section can be obtained when we cut a rectangular prism with a plane that is parallel to the faces. This cross-section is the easiest to obtain since it can be obtained when the plane is oriented in different directions.

For example, we can get a rectangular cross-section when the plane is parallel to the front faces as shown in the diagram:

cross section of a rectangular prism

If the plane is parallel to the lateral faces, we obtain the rectangular cross-sections shown in the following diagram:

cross section of a rectangular prism2

Also, we can obtain rectangular cross-sections when the plane is parallel to the bases of the prism:

cross section of a rectangular prism3

Finally, in the following diagram, we can see that we can obtain rectangular cross-sections even when the plane that cuts the prism has an inclination with respect to all faces.

cross section of a rectangular prism4

Triangle cross-section

A triangular cross-section can be obtained when we cut a rectangular prism with a plane such that the plane intersects three edges of the prism.

triangular cross section of a rectangular prism

Additionally, if the distance from the central vertex to the point of intersection is the same for all three edges, the triangle formed will be equilateral.


Pentagonal cross-section

When a plane intersects five edges of a rectangular prism, the cross-section formed will be a pentagon. However, the pentagon formed will be irregular in most cases.

pentagonal cross section of a rectangular prism

Hexagonal cross-section

When a plane intersects six edges of a rectangular prism, the cross-section formed will be a hexagon. In most cases, the hexagon formed will be irregular.

hexagonal cross section of a rectangular prism

See also

Interested in learning more about cross-sections of geometric figures? Take a look at these pages:

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