# Pyramid

A **pyramid** is a three-dimensional polyhedron-shaped structure with only one polygonal base and has triangular sides. It has a flat polygon base. All the other faces are triangles and are called lateral faces. The number of lateral faces equals the number of sides on its base. Its edges are the line segments formed by two intersecting faces. The vertex is the common point where three or more edges combine. Except for the base, all the faces connect at a vertex at the top called the apex. The apex stands opposite to the base and provides it a shape.

## Differences between Pyramid and Prism

Pyramids and prisms are both three-dimensional figures with polygonal bases and flat faces. But they have several differences, such as:

- While a pyramid has a single base, a prism has two of them.
- A pyramid has triangular faces, but a prism has rectangular faces.
- A pyramid has an apex. A prism has no apex.

**Pyramid Formula : **

**Surface area of the Pyramid : **

The lateral surface area of a regular pyramid is the sum of the areas of the lateral faces of the pyramid.

Lateral Surface Area =$\frac{1}{2}$×p×l

Where p-the perimeter of the base; l-slant height

**Total Surface Area of a Regular Pyramid**

It is the sum of the areas of lateral faces of the pyramid and base of the pyramid.

### Total Surface Area** **=**$\frac{1}{2}$**×p×l+B

Where p-the perimeter of the base; l-slant height; B-the area of the base

**Volume of the Pyramid**

Volume of a 3 -dimensional solid is the amount of space occupies by the solid.

The volume of a Pyramid=$\frac{1}{2}$×Base Area×Height

**Types of Pyramid**

**Square Pyramid**

A square pyramid has a square base, triangular faces as 4 and an apex. The Square Pyramid formulas are,

- Base Area of a Square Pyramid = b
^{2} - Surface Area of a Square Pyramid = 2 × b × s +b
^{2} - Volume of a Square Pyramid=$\frac{1}{3}$ × b
^{2 }× h

Where b-base length; s-slant height; h-height

**Triangular Pyramid**

A triangular pyramid is a pyramid, which has triangular faces, and a triangular base. The Triangular Pyramid formulas are,

- Base Area of a Triangular Pyramid=$\frac{1}{2}$×a×b
- Surface Area of a Triangular Pyramid=$\frac{1}{2}$×a×b+$\frac{3}{2}$×b×s
- The volume of a Triangular Pyramid=$\frac{1}{6}$×a×b×h

Where a-apothem length; b-base length; s-slant height; h-height

**Pentagonal Pyramid**

The Pentagonal pyramid has a pentagonal base, triangular faces as 5 and an apex. The Pentagonal Pyramid Formulas are,

- Base Area of a Pentagonal Pyramid=$\frac{5}{2}$×a×b
- Surface Area of a Pentagonal Pyramid=$\frac{5}{2}$(a×b+b×s)
- The volume of a Pentagonal Pyramid=$\frac{5}{6}$×a×b×h

Where a-apothem length; b-base length; s-slant height; h-height

## Number of Faces, Vertices, and Edges

A pyramid with a base of n sides has n+1 faces, n+1 vertices, and 2n edges.

## What Are Right and Oblique Pyramids?

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 |
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## What Are Regular and Irregular Pyramids?

A pyramid with regular polygon as a base is called a regular pyramid. It means all the sides and angles of the base polygon are equal.

Regular Pyramid | Irregular Pyramid |
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