Volume of Triangular Pyramid
What do we mean by the volume of a triangular pyramid and how do we define it? Volume is nothing but the space an object occupies. An object with a larger volume occupies more space. So the volume of a triangular pyramid will be the space occupied by the triangular pyramid.
Let's learn how to find the volume of a triangular pyramid in detail here with the help of few solved examples and practice questions.
1.  What Is a Triangular Pyramid? 
2.  Volume of a Triangular Pyramid Formula 
3.  How to Find the Volume of a regular Triangular Pyramid? 
4.  FAQs 
What Is a Triangular Pyramid?
A triangular pyramid is a threedimensional shape having all faces as triangles. A triangular pyramid is a pyramid with a triangular base and bounded by four triangular faces where 3 faces meet at one vertex. Did you know that one of the oldest pyramid structures known to man is the "Great Pyramid of Giza?" It was constructed around 2550 BC, in Egypt. They are considered among the seven wonders of the world. They are pyramids, alregular, but are they triangular pyramids as well?
In a regular triangular pyramid, all faces are equilateral triangles and are known as tetrahedrons. In a regular triangular pyramid, the base is an equilateral triangle while other faces are isosceles triangles. In an irregular triangular pyramid, a scalene or isosceles triangle forms the base.
What Are the Parts of a Triangular Pyramid?
Here are the parts of a triangular pyramid:
 It has 4 faces, 6 edges, and 4 corners.
 At each of its vertex, 3 edges meet.
 A triangular pyramid has no parallel faces.
 A regular triangular pyramid has equilateral triangles for all its faces. It has 6 planes of symmetry.
 Triangular Pyramids are found as regular, irregular, and regularangled.
Volume of a Triangular Pyramid Formula
The volume of a triangular pyramid is the number of unit cubes that can fit into it. The unit of volume is "cubic units". For example, it can be expressed as m^{3}, cm^{3}, in^{3}, etc depending upon the given units.
Let us see how to find the formula of the volume of a triangular pyramid.
The volume of a triangular pyramid can be easily found out by just knowing the base area and its height:
\(\begin{align} \frac{1}{3} \text { Base Area} \times \text {Height} \end{align}\)
Now consider a regular triangular pyramid made of equilateral triangles of side \(a\).
Regular Triangular Pyramid Volume:
\(\text{Volume} =\begin{align} \frac{a^3}{6\sqrt{2}}\end{align}\)
How to Find the Volume of a Triangular Pyramid?
As we learned in the previous section, the volume of a triangular pyramid could be found using two formulas. Thus, we follow the below steps to find the volume of a triangular pyramid.
 Step 1: Determine the base area and the height of the pyramid.
 Step 2: Find the volume using the general formula \(\text{V} = \dfrac{1}{3} \times \text {Base Area} \times \text {Height}\) or \(\text{V} =\begin{align} \frac{a^3}{6\sqrt{2}}\end{align}\) when the edge length 'a' of triangular face is known.
 Step 3: Represent the final answer with cubic units.
Solved Examples on Volume of a Triangular Pyramid

Example 1
Find the volume of a regular triangular pyramid with a side length measuring 5 units.
(Round off the answer to 2 decimal places.)
Solution:
We know that for a triangular pyramid whose side is \(a\), the volume is:
\(\begin{align}\text{Volume} = \frac{a^3}{6\sqrt{2}}\end{align}\)
Substituting \(a\) as 5 we get
\[\begin{align}
\text{Volume} &= \frac{5^3}{6\sqrt{2}} \\\\
&=\frac{125}{8.485} \\\\
&\approx 14.73
\end{align}\] 
Answer: Volume of the triangular pyramid is 14.73 units^{3}.
Example 2
What is the volume of a triangular pyramid whose base area is 9 in^{2} and height is 4 inches?
Solution:
Given,
Base area = 9 in^{2}
Height = 4 inAs we know,
The volume of a triangular pyramid = 1/3 × Base Area × HeightPutting the values in the formula: 1/3 × 9 × 4 = 12 in^{3}
Answer: The volume of the given triangular pyramid is 12 in^{3}.
Here are a few activities for you to practice.
Select/type your answer and click the "Check Answer" button to see the result.
FAQs on Volume of a Triangular Pyramid
What Is a Triangular Pyramid?
A triangular pyramid is a threedimensional shape having all faces as triangles.
How Do You Find the Volume of a Triangular Pyramid?
The volume of a triangular pyramid can be easily found out by just knowing the base area and its height = 1/3 × Base Area × Height
What Is the Volume of a Regular Triangular Pyramid Calculator?
Regular triangular pyramid volume:
\(\text{Volume} =\begin{align} \frac{a^3}{6\sqrt{2}}\end{align}\)
where 'a' is the edge of the trianglular (equilateral) faces.
What Units Are Used With the Volume of the Triangular Pyramid?
In the metric system of measurement, the most common units of volume are milliliters and liters.
How Do You Find the Volume of Prisms?
The formula for the volume of a prism is V = B × h, where B is the base area and h is the height.
What Is the Formula for Finding the Volume of a Triangular Pyramid?
The volume of a triangular pyramid is found using 1/3 × Base Area × Height.