# Definition:Pyramid

## Definition

Let $P$ be a polygon.

Let $Q$ be a point not in the plane of $P$.

From each vertex of $P$, let lines be drawn to $Q$.

The polyhedron which is contained by $P$ and the triangles formed by the sides of $P$ and the lines to $Q$ is a **pyramid**.

In the words of Euclid:

(*The Elements*: Book $\text{XI}$: Definition $12$)

### Apex of Pyramid

The vertex of a pyramid which is the common vertex of its triangular faces is called the **apex** of the pyramid.

In the above diagram, $Q$ is the **apex**.

### Base of Pyramid

The polygon of a pyramid to whose vertices the apex is joined is called the **base** of the pyramid.

In the above diagram, $ABCDE$ is the **base** of the pyramid $ABCDEQ$.

### Lateral Face of Pyramid

The triangular faces of a pyramid which lead to the apex are called the **lateral faces** of the pyramid.

In the above diagram, $ABQ$ and $DEQ$, for example, form two of the $5$ **lateral faces** of the pyramid $ABCDEQ$.

### Height of Pyramid

The **height** of a pyramid is the length of the perpendicular from the plane of the base to its apex.

In the above diagram, $h$ is the height.

## Also see

- Definition:Tetrahedron: a
**pyramid**whose base is a triangle.

- Definition:Square Pyramid: a
**pyramid**whose base is a square.

- Results about
**pyramids**can be found**here**.

## Linguistic Note

The word **pyramid** derives directly from the Classical Greek **πυραμίς** (**pyramis**) whose derivation is unknown.

In natural language the word usually refers to a square pyramid, and usually calls to mind the Great Pyramid of Giza.

## Sources

- 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next):**pyramid** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**pyramid**