# Pyramid vs. Prism: What's the Difference?

Edited by Aimie Carlson || By Harlon Moss || Published on December 17, 2023
A pyramid is a 3D shape with a polygonal base and triangular faces meeting at a point, whereas a prism is a 3D shape with two identical polygonal bases connected by rectangular faces.

## Key Differences

Pyramids have a base that can be any polygon, and their sides are triangles converging to a single point. This point is not in the same plane as the base. Prisms, in contrast, have two bases that are congruent, parallel polygons, and their sides are parallelograms or rectangles, depending on the angle of the side edges.
In a pyramid, the number of faces depends on the base's shape; for example, a square base results in four triangular faces, plus the base. In a prism, the number of faces is always two more than the number of sides on the base; for instance, a triangular prism has five faces in total.
The volume of a pyramid is calculated as one-third the base area times the height, where the height is perpendicular from the base to the apex. In contrast, the volume of a prism is the base area times the height, where the height is the perpendicular distance between the two bases.
Pyramids are often associated with ancient structures, especially in Egypt and Mesoamerica, symbolizing architectural and cultural significance. Prisms are commonly referenced in optics and physics, particularly for dispersing light into a spectrum or reflecting images.
In geometry education, pyramids are used to teach about vertex figures and Euler's formula. Prisms are used to teach about surface area, volume, and the properties of different polygons, as the type of the prism changes with the shape of the base.

## Comparison Chart

### Shape of Faces

Triangular sides converging to a point
Rectangular or parallelogram sides

### Base Configuration

Polygonal (any type)
Two congruent, parallel polygonal bases

### Volume Calculation

One-third base area times height
Base area times height

### Cultural/Practical Significance

Often associated with ancient architecture and monuments
Commonly used in optics and physics

### Educational Focus

Vertex figures, Euler's formula
Surface area, properties of polygons

## Pyramid and Prism Definitions

#### Pyramid

A structure or object with a polygonal base and triangular faces converging to a point.
The Great Pyramid of Giza is a classic example of a square-based pyramid.

#### Prism

An optical element that refracts or disperses light.
A glass prism can split white light into a spectrum of colors.

#### Pyramid

A monumental structure with a square or triangular base and sloping sides.
Ancient Mayan temples often featured pyramid designs.

#### Prism

A polyhedron with two congruent faces and other faces parallelograms.
In geometry, we studied how the properties of a triangular prism differ from a rectangular one.

#### Pyramid

A polyhedron with a base of any polygon and sides of triangles.
A tetrahedron is a type of pyramid with a triangular base.

#### Prism

A solid geometric figure with two identical, parallel polygonal bases connected by faces.
A rectangular prism is a common shape in everyday objects like boxes.

#### Pyramid

A shape in geometry with a base and triangular sides.
In math class, we learned how to calculate the volume of a pyramid.

#### Prism

Any shape with identical ends and flat sides.
The prism-shaped award was made of crystal.

#### Pyramid

An item or form resembling a pyramid in shape.
She stacked the cans in a pyramid shape.

#### Prism

A transparent optical element with flat, polished surfaces.
He used a prism in his physics experiment to demonstrate light refraction.

#### Pyramid

A solid figure with a polygonal base and triangular faces that meet at a common point.

#### Prism

A solid figure whose bases or ends have the same size and shape and are parallel to one another, and each of whose sides is a parallelogram.

#### Pyramid

Something shaped like this polyhedron.

#### Prism

A transparent body of this form, often of glass and usually with triangular ends, used for separating white light passed through it into a spectrum or for reflecting beams of light.

## FAQs

#### Can a pyramid have a circular base?

No, a pyramid must have a polygonal base, not a circular one.

#### What defines a pyramid in geometry?

A pyramid has a polygonal base and triangular sides that meet at a common point.

#### Are all sides of a prism the same shape?

The end faces are identical polygons, but the side faces are rectangles or parallelograms.

#### What is a prism in geometric terms?

A prism is a polyhedron with two parallel, identical polygonal bases and rectangular sides.

#### What's the difference in volume calculation between a pyramid and a prism?

A pyramid's volume is one-third the base area times the height, while a prism's volume is the base area times the height.

#### What are the practical applications of prisms?

Prisms are used in optics, such as in cameras, binoculars, and periscopes.

#### Do pyramids always have a square base?

No, pyramids can have any polygonal shape as a base.

#### What's the difference between a prism and a cylinder?

A prism has flat polygonal ends and a cylinder has circular ends.

#### What's an example of a pyramid in nature?

A mountain can naturally form a pyramid-like shape.

#### Do prisms always have straight edges?

Yes, the edges of a prism are straight lines.

#### What is a common use of a prism in photography?

Prisms are used in cameras for image correction and light manipulation.

#### Is a pyramid always associated with burial structures?

Not always; pyramids are also significant in geometry and have various modern uses.

#### How many edges does a triangular pyramid have?

A triangular pyramid has six edges.

#### Are all pyramids three-dimensional?

Yes, pyramids are three-dimensional geometric figures.

#### Can prisms be used to change the direction of light?

Yes, prisms can refract or reflect light, changing its direction.

#### Are all faces of a pyramid triangles?

Except for the base, all faces of a pyramid are triangles.

#### How does light dispersion work in a prism?

A prism refracts light, separating it into its component colors.

#### Can prisms have triangular bases?

Yes, a triangular prism has triangular bases.

#### Can a pyramid have more than four sides?

Yes, the number of sides depends on the shape of the base.

#### Is a pyramid considered a polyhedron?

Yes, a pyramid is a type of polyhedron.