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# Triangular Pyramid Formula | Volume & Surface Area of a Triangular Pyramid

## What is Triangular Pyramid?

Have you seen a real pyramid in life? Think of great pyramids of Egypt once and you will recall the concepts yourself. A pyramid is a three-dimensional shape here with polygon as the based triangle as three sides that are meeting at a single point.

Here, the triangular sides are named as faces and the bottom polygon is recalled as base of the pyramid. The number of sides for a pyramid would be equal to the total number of sides or triangular faces of a pyramid. The common point where all triangular faces meet is called the Apex.

### Triangular Pyramid Formula

A pyramid could be any polygon as a base, hence the structure of base is not fixed here. Let us take an example where base is triangular. Since we know that a triangle has three sides then the triangular pyramid would have three triangular bases in that case. They are common in other areas too like architecture, art, designing or more.

$\ Volume\;of\;a\;triangular\;pyramid=\frac{1}{3}Base\;Area\times Height$

$\ Surface\;area=Base\;Area+\frac{1}{2}Perimeter\times Side\;length$

Now there are two more possible cases for the triangular pyramid. These are regular pyramid and non-regular pyramid. A regular pyramid has a base whose all three sides are equal in length and for a non-regular pyramid; the base has sides of different lengths. Further, you could calculate the volume or surface area for a triangular pyramid too. You have to use the triangular pyramid formula as given in mathematics. Volume for a pyramid could be defined as the total space occupied by the pyramid. And the surface area could be given as total area of all its faces and base combined.

### Examples of Triangular Pyramid

Question 1: Find the volume of a triangular pyramid when base area is 9 cm2 and height is 4 cm ?

Solution:
Given,
Base area = 9 cm2 Height = 4 cm

As we know, $\ Volume\;of\;a\;triangular\;pyramid=\frac{1}{3}\;Base\;Area\times Height$ According to the formula: $\ \frac{1}{3}\times9\times4=12\,cm^{2}$