Mensuration - Pyramid

What is a Pyramid?

A Pyramid is a three dimensional polyhedron, such that:

• its base is a polygon (of any number of sides), and
• the other faces are triangles with a common vertex, called the apex.

A pyramid with n-sided base has n + 1 vertices, n + 1 faces, and 2n edges.
For example, in the above figure the base has 4 sides, and so the pyramid has 5 vertices, 5 faces, and 8 edges.

Right Pyramid: It is a pyramid whose axis is perpendicular to its base.

Regular Pyramid: It is a pyramid whose base is a regular figure, i.e. all sides of its base are equal.

Formulae related to Pyramids

Formula 1: Slant Height

The slant height of a regular right-pyramid is the line-segment joining the vertex to the mid-point of anyone of the sides of the base.

In the above figure, O is the centre of the base and AM is the slant height.
Also, as ∆AOM is a right-angled triangle, so by Pythagoras theorem:
$AM^2 = AO^2 + OM^2$

Formula 2: Volume

Volume of a Pyramid = $\frac{1}{3}$ × Base Area × Height

Formula 3: Surface Area

Lateral surface area = $\frac{1}{2}$ × Perimeter of base × Slant height

Total surface area = Lateral surface area + Area of base

Types of Pyramids as per their Base

We already know that, base of a pyramid is a polygon of any number of sides.

So, based on the kind of base, we get various types of pyramids.

• Triangular pyramid (Tetrahedron) - have a triangular base with 3 sides.
• Rectangular or Square pyramid - have a square/rectangular base with 4 sides.
• Pentagonal pyramid - have a pentagonal base with 5 sides.
• Hexagonal pyramid - have a hexagonal base with 6 sides.
• and so on …..

We will study some of these pyramids in more detail in subsequent articles.