Geometry - What is a Prism in Math?

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     Prisms are polyhedrons with two parallel faces.  Their faces are called ‘bases’.  The other faces are parallelograms.  Every prism must have two bases (a top and bottom), that are identical, parallel polygon shapes. 

     The shape of a prism’s base determines its name.  For example, we can have rectangular prisms, triangular prisms, pentagonal prisms, and so on.  A rectangular prism will have two bases that are rectangles and a triangular prism will have two bases that are triangles, etc....

     A closed, irregular shape that is not a true polygon can become an "irregular" prism as long as both bases are identical and a cross section anywhere along the length matches the base.

     We can create a prism because any two-dimensional (2-D) shape can be expanded into a three-dimensional (3-D) prism. Duplicate the 2-D shape to create the two bases, move them a distance apart, then join each corner point on the first shape to the same point on the second shape to create the sides.  Imagine unfolding the sides of a prism to make a two dimensional figure.  This figure, which would appear to have flaps, is called a ‘net’.  We can fold the sides of nets together to create three dimensional figures such as prisms.

    Since prisms are three dimensional figures, their volume can be measured.  We can measure the volume of prisms by multiplying the base time the height.

Volume = Area × Length

For example: What is the volume of a prism whose ends are 25 cm² and which is 12 cm long:

Answer: Volume = 25 cm² × 12 cm = 300 cm³

Volume is always expressed in units cubed (³).

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