Prisms

A prism is a solid object with:

  • identical ends
  • flat sides
  • and the same cross section all along its length !

 

A cross section is the shape made by cutting straight across an object.

The cross section of this object is a triangle ...

.. it has the same cross section all along its length ...

... and it's a triangular prism.


Try drawing a shape on a piece of
paper (using straight lines)

Then imagine it extending up from the sheet of paper ...
... that's a prism !

Drawing a Prism

Prism not cylinder

No Curves!

A prism is a polyhedron, which means all sides are flat!

No curved sides.

For example, a cylinder is not a prism, because it has curved sides.

Bases


The ends of a prism are parallel
and each one is called a base.

Sides


The sides of a prism are parallelograms
(4-sided shape with opposites sides parallel)

These are all Prisms:


Square Prism: Cross-Section:

Cube: Cross-Section:
(yes, a cube is a prism, because it is a square
all along its length)
(Also see Rectangular Prisms )

Triangular Prism: Cross-Section:

Pentagonal Prism: Cross-Section:


and more!

Regular and Irregular Prisms

All the previous examples are Regular Prisms, because the cross section is regular (in other words it is a shape with equal edge lengths, and equal angles.)

Here is an example of an Irregular Prism:

Irregular Pentagonal Prism:    

 
  Cross-Section
It is "irregular" because the
cross-section is not "regular" in shape.

Volume of a Prism

The Volume of a prism is the area of one end times the length of the prism.

Volume = Area × Length

Example: What is the volume of a prism whose ends have an area of 25 m2 and which is 12 m long:

Answer: Volume = 25 m2 × 12 m = 300 m3

(Note: we have an Area Calculation Tool)

More About The Sides

The sides of a prism are parallelograms
(4-sided shape with opposites sides parallel)

 

A prism can lean to one side, making it an oblique prism, but the two ends are still parallel, and the sides are still parallelograms!

 

But if the two ends are not parallel it is not a prism.