# Pyramid

In Geometry, a pyramid is a space figure that has a polygon as its base and triangles as all its other faces. All the faces of a pyramid, except its base, intersect at a common point. The following are some examples.

Outside of geometry, the term "pyramid" is often used in reference to the pyramids of Egypt, which served as tombs for ancient Egyptian kings. Pyramids are sometimes used in modern construction, as in the Louvre, a famous museum in Paris.

## Properties of a pyramid

The faces of a pyramid that are not its base are called lateral faces. The number of lateral faces in a pyramid is the same as the number of sides in its polygonal base. The line segments created by two intersecting faces are called edges. The vertices are points where three or more edges meet. The vertex opposite the base is called its apex. The apex is often thought of as the "top" of the pyramid. It is also the common point shared by all the lateral faces of the pyramid.

The square pyramid above has a total of five faces. It has 4 lateral faces that are triangles and its base is a square. A square pyramid has 8 edges and 5 vertices.

Any cross section that is parallel to the base of a pyramid forms a polygon that is similar to the base.

The three triangles, shaded in green, formed by cross sections parallel to the base of the triangular pyramid above, are similar (same shape but not the same size) to the pyramid's base.

## Pyramid classifications

We typically name a pyramid based on the shape of its polygonal base. The following are some examples.

### Right pyramid and oblique pyramid

If the apex of a pyramid is directly above the center of the base, it is a right pyramid. Otherwise, it is an oblique pyramid.

Right pyramid | Oblique pyramid |
---|---|

A perpendicular line from the apex intersects the base at its center. | A perpendicular line from the apex does not intersect the base at its center. |

### Regular pyramid

If the base of a pyramid is a regular polygon, it is a regular pyramid. Otherwise, it is an irregular pyramid. Often, a regular pyramid is implied to be a right pyramid.

Regular pyramid | Irregular pyramid |
---|---|

The base of the square pyramid above is a square, which is a regular polygon. | The base of the trapezoidal pyramid above is a trapezoid, which is an irregular polygon. |

### Tetrahedron

A tetrahedron is a special pyramid in that all of its faces are triangles. It is the only type of pyramid in which any of its faces can be the base and any of its vertices can be the apex.

## Volume of a pyramid

The volume of pyramid is:

B is the area of the base and h is the height of the pyramid, which is the distance from its apex to its base.