# Pyramids

When we think of pyramids we think of the **Great Pyramids of Egypt**.

They are actually * Square Pyramids*, because their base is a Square.

## Parts of a Pyramid

A pyramid is made by connecting a **base** to an **apex**

The base is a polygon (flat with straight edges) and all other faces are triangles. No curves!

## Types of Pyramids

There are many types of Pyramids, and they are named after the shape of their base.

Pyramid | Base | |

Triangular Pyramid: | ||
---|---|---|

Square Pyramid: | ||

Pentagonal Pyramid: | ||

... and so on ... |

Fly through some pyramids here.

## Right vs Oblique Pyramid

This tells us where the top (apex) of the pyramid is. When the apex is directly above the center of the base it is a **Right Pyramid**, otherwise it is an **Oblique Pyramid**.

Right Pyramid | Oblique Pyramid |
---|

## Regular vs Irregular Pyramid

This tells us about the **shape of the base**. When the base is a regular polygon it is a **Regular Pyramid**, otherwise it is an **Irregular Pyramid**.

Regular Pyramid | Irregular Pyramid |
---|---|

Base is Regular | Base is Irregular |

## Area and Volume

### The Volume of a Pyramid

× [Base Area] × Height^{1}/_{3}

### The Surface Area of a Pyramid

When all side faces are the same:

- [Base Area] +
× Perimeter × [Slant Length]^{1}/_{2}

When side faces are different:

- [Base Area] + [Lateral Area]

### Notes On Surface Area

The Surface Area has two parts: the area of the base (the * Base Area*), and the area of the side faces (the

*).*

**Lateral Area** For * Base Area* :

It depends on the shape, there are different formulas for triangle, square, etc. See Area for formulas, or our Area Calculation Tool

For * Lateral Area* :

When all the side faces are the same:

- Multiply the perimeter by the "slant length" and divide by 2. This is because the side faces are always triangles and the triangle formula is
*"base times height divided by 2"*

But when the side faces are different (such as an "irregular" pyramid) we must add up the area of each triangle to find the total lateral area.