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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:

A pyramid is a solid figure, contained by planes, which is constructed from one plane to one point.

(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 $ABCDEQ$.

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

  • 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.