# Pyramid Shape

By the end of this lesson, you will be able to

- define a pyramid
- describe the characteristics of base and faces of a pyramid.
- derive the formula for surface area of a pyramid.
- dermine the formula for volume of a pyramid.

## Pyramid

A pyramid is a polyhedron in which the base is a polygon and all other lateral faces are triangles meet at a fixed common point on another surface above the base.

A pyramid is showing its base and faces.

The lateral faces must be three or more triangles. The fixed common point is called the apex of the pyramid. The number of literal surface is at least three or more. So, a pyramid is a special type of polyhedron with polygonal base and literal faces of triangle shape in 3-dimensional space.

Thus a pyramid must have

- a polygonal base
- 3 or more triangular faces
- an apex

## Base of the Pyramid

The base on which pyramid lies is called the base of the pyramid. The base of a pyramid is a polygon. And this polygon may be regular or irregular. If the base is a pentagon of a pyramid, there are 5 lateral faces and 10 edges. Thus the number of sides of the base is equal to the number of lateral faces and half the number of edges.

## Faces of Pyramid

The lateral faces of a pyramid are always triangles. But these faces may be congruent or not depending upon the base. If the base is a regular polygon, all triangular faces are congruent.

## Height of Pyramid

The perpendicular from the apex to the base is called the height of the pyramid.

A pyramid is showing its height.

## Type of Pyramid

There are several type of pyramid in real life like

- regular pyramid
- irregular pyramid
- right pyramid
- oblique pyramid

### Regular pyramid

A regular pyramid is a pyramid in which the base is a regular polygon. The regular pyramids are mostly used.

### Irregular pyramid

A pyramid is said to be irregular if the base is a irregular polygon.

### Regular Pyramid Example

### Right pyramid

A pyramid is said to be right if the perpendicular from the apex to the base passes through the center of the base. The center is the point of intersection of diagonals of the regular polygonal base. Hence a regular pyramid is a right pyramid.

### Oblique pyramid

If the perpendicular drawn from the vertex to the base passes through the point other than center of the base is called the oblique pyramid. A pyramid is not right is an oblique pyramid. Therefore, all the pyramids except right pyramid are oblique pyramid.

An oblique pyramid showing its base, faces and edges.