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What is a Rectangular Prism? - Definition & Examples

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  • 0:05 Prisms
  • 0:39 Prism Rules
  • 2:24 Oblique Prisms
  • 2:47 Rectangular Prisms
  • 3:42 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, you will learn what prisms are and what makes rectangular prisms unique. There are several rules that identify a three-dimensional shape as a prism. You will also consider a few everyday items as examples of rectangular prisms.

Prisms

Prisms are a certain kind of shape, but what makes them stand out? A prism is two polygons, or multiple-sided closed shapes, joined together to form an enclosed three-dimensional shape. For example, a box is a prism because it consists of two squares or rectangles joined together to make the enclosed three-dimensional figure seen here:

Two squares joined together to form a prism.
rectangular box

Two-dimensional shapes make the flat top and bottom sides, or faces, of a prism.

So any box, stacks of Post-It Notes, and even legal pads are all prisms because they're three-dimensional objects with congruent polygons as faces.

Prism Rules

There are five rules for identifying a prism:

Rule 1: is that the faces of a prism must be polygons. So even though it may seem that cylinders would be prisms, they don't fit the definition. This is because their faces are circles or ovals, which don't have sides and are therefore not polygons. So a can isn't a prism. No sides, no polygons, no prism.

No sides, no polygons, no prism!
tin can

A prism can have triangles as faces.

Prism with triangular faces.
Prism with triangular faces.

Rule 2: states that the sides of a prism must be parallelograms. Parallelograms are quadrilaterals whose opposite sides are parallel. Consider a box and a triangular prism, all of their sides are parallelograms.

Rule 3: The third rule says a prism's faces must be parallel. If one face lies at an angle to the other, they will at some point intersect, and the figure is not a prism. Also, if the faces aren't parallel, the sides won't be parallelograms.

In this figure, for example, the rear face lies at an angle compared to the front face. As a result, two of the sides are not parallelograms. Non-parallel faces create sides that are not parallelograms.

Non-parallel faces create sides that are not parallelograms.
almost prism with skewed faces

Rule 4: states that the bases must be congruent. Congruent means the exact same shape and size.

A figure that has differently shaped faces creates sides that are not parallelograms. Since the faces are not congruent, this figure isn't a prism.

This is not a prism because the faces are not congruent.
non-congruent faces

Rule 5: Lastly, rule five says if a cross-section is taken of a prism parallel to its faces, the cross-section would be congruent with the prism's faces. This happens because the faces are congruent and parallel. This is true no matter where you slice it.

Think of it like a loaf of bread. If it's sliced parallel to the ends, no matter where you cut, the slices will have the same shape.

The slices, or cross-sections, all have the same shape as the loaf
sliced bread loaf

Oblique Prisms

With all these rules, it's important to realize that there is something that isn't a rule. The angles between the sides and the faces do not have to be right angles. An oblique prism has slanted sides, but the faces are still congruent and parallel.

An oblique prism has non-right angles between the sides and faces.
a slanted or oblique prism

Although this type of prism's sides slant, its pentagonal faces are congruent and parallel and its sides are still parallelograms.

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