Understanding Prism In Mathematics
A prism is a polyhedron, meaning it is a 3D shape made up of flat faces. It has two parallel, congruent bases, and its other faces are parallelograms or rectangles.
One of the defining features of a prism is that its cross-section remains the same all the way through when sliced parallel to its bases. This property distinguishes prisms from other 3D shapes like pyramids, which taper to a single point.
Key Concepts Related To Prisms
Naming Prisms
Prisms are named based on the shape of their bases. This means the name of a prism tells us what kind of polygon forms its two identical bases:
| Prism Name | Shape of Base |
| Triangular prism | Triangle |
| Rectangular prism | Rectangle |
| Pentagonal prism | Pentagon |
| Hexagonal prism | Hexagon |
NOTE: Prisms can have any type of polygonal base, as long as there are two identical bases and the sides remain flat.
Prisms and Volume
The volume of a prism is found using the formula, V = Bh, where B is the area of the base, and h is the height of the prism.
This formula connects 2D and 3D mathematical thinking because students must:
- Find the area of the base (B), a two-dimensional calculation.
- Extend that area into the third dimension (h) to determine volume.
This helps students understand how stacking layers of a 2D shape creates a 3D object, reinforcing the relationship between area and volume.
The Net of a Prism
The net of a prism is a 2D pattern that can be folded into the 3D shape. Every prism’s net consists of two identical polygonal bases (matching the prism’s name), and rectangular or parallelogram lateral faces that connect the bases.
Studying nets helps students visualize how a 3D shape is constructed from flat surfaces and connects to concepts like surface area and spatial transformations.
Common Misconceptions About Prisms
Misconception: Pyramids Are Prisms
Pyramids are often mistaken for prisms, but they are different in a few key ways.
First, prisms have two parallel bases, while pyramids have only one base with triangular faces meeting at a single point (apex).
Next, the lateral faces of a prism are rectangles or parallelograms, while the lateral faces of a pyramid are always triangles.
Finally, a prism has a uniform cross-section throughout, while a pyramid does not.
Encouraging students to compare prisms and pyramids side by side, exploring their nets and cross-sections, helps them understand these structural differences.
