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What is a rectangular prism?

As you saw with the watermelons, prisms are all around us, especially rectangular prisms. You can probably recognize a prism when you see one, but do you know what makes a prism a prism? Can you tell a rectangular prism from another sort of prism? Let's see how to identify them.


Prisms

  • are three-dimensional
  • have a set of exactly two faces that are congruent and parallel polygons, which are called bases
  • have faces that are parallelograms
  • are polyhedrons

The faces of the prism are usually congruent, but not always. Prisms are identified by the shape of their bases. If the bases are in the shape of a triangle, then it's a triangular prism. Bases in the shape of a pentagon define a pentagonal prism.

Now, let's take a look at this slide show to see some things that are prisms.

Here is an example of a prism.

prism

What kind of prism is it?

The bases are pentagons. This is a pentagonal prism.

prism

What kind of prism is this?

This is a hexagonal prism. The bases are hexagons.

For this lesson, our focus will be on rectangular prism. Here is an example of a right rectangular prism. A right prism has bases and faces that are all rectangles. It kind of looks like a shoe box. The faces are perpendicular to the bases. In other words, they form right angles.

right prism

oblique rectangular prism

Here we have a rectangular prism. It looks like a box that's lost its shape, like it's been pushed over a bit. Oblique rectangular prisms have faces that are not strictly perpendicular to the bases. In other words, the faces aren't straight up and down. The faces are at a slant, or angle, other than 90°.

sijon [CC-BY-SA-2.0 (http://creativecommons.org/licenses/by-sa/2.0)], via Wikimedia Commons

This is the front face of a building that's in the shape of a rectangular prism. Do you think the building is a right rectangular prism or an oblique rectangular prism?

This building is an oblique rectangular prism. It looks as though it has been pushed to the right.

By Kure (UserKurefile) [CC-BY-SA-2.5 (http://creativecommons.org/licenses/by-sa/2.5)], via Wikimedia Commons

This building actually seems to be made of 1 big rectangular prism with 2 smaller rectangular prisms on the roof. Do you think these prisms are right rectangular prisms or oblique rectangular prisms?

These are plain, straight-up-and-down, right rectangular prisms. These prisms are standing straight with no slant to the left or to the right.

Now that you've gotten better acquainted with rectangular prisms, let's see how to calculate their volume.