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 the Volume of Triangular Pyramid? 
2.  Volume of a Triangular Pyramid Formula 
3.  How to Find the Volume of a regular Triangular Pyramid? 
4.  FAQs on Volume of Triangular Pyramid 
What is the Volume of Triangular Pyramid?
The volume of a triangular pyramid is the space occupied by a triangular pyramid in a threedimensional plane. The volume of a triangular pyramid is the total number of unit cubes that can fit into the shape and is represented in "cubic units". Commonly the units used to express the volume of a triangular pyramid as m^{3}, cm^{3}, in^{3}, etc.
A triangular pyramid is a threedimensional shape having all faces as triangles. A triangular pyramid is bounded by four triangular faces and has a triangular base, the 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, irregular, but are they triangular pyramids as well?
In a regular triangular pyramid, all faces are equilateral triangles and is known as a tetrahedron. 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.
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 can be easily found out by just knowing the base area and its height and is given as Volume of a triangular pyramid = (1/3) Base Area × Height
Depending upon the type of triangular base and known parameters, we can apply any of the area of triangle formulas to calculate the base area.
Now, consider a regular triangular pyramid made of equilateral triangles of side 'a'. 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:
(1/3) Base Area × Height
Now consider a regular triangular pyramid made of equilateral triangles of side 'a'.
Regular Triangular Pyramid Volume: Volume = a^{3}/6√2 cubic units
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, V = (1/3) Base Area × Height, or V = a^{3}/6√2 cubic units when the edge length 'a' of the triangular face is known.
 Step 3: Represent the final answer with cubic units.
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:
The volume of triangular pyramid = a^{3}/6√2 cubic unitsSubstituting 'a' as 5 we get
Volume = a^{3}/6√2Substituting 'a' with 5 we get,
Volume = 5^{3}/6√2 = 125/8.485 ≈ 14.73Answer: The 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 × Height
Putting the values in the formula: 1/3 × 9 × 4 = 12 in^{3}Answer: The volume of the given triangular pyramid is 12 in^{3}.
FAQs on Volume of a Triangular Pyramid
What Is the Volume of Triangular Pyramid?
Volume of a triangular pyramid is defined as the total space occupied by the shape in a threedimensional plane. 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. We can directly apply the following formula for this case,
The volume of Triangular Pyramid = 1/3 × Base Area × Height
What Is the Formula for Finding the Volume of a Triangular Pyramid?
The formula used to calculate the volume of a triangular pyramid is given as, 1/3 × Base Area × Height. Here, the base area can be found using any of the area of triangle formulas depending upon the type of triangular base and known parameters.
What Is the Volume of a Regular Triangular Pyramid?
The volume of a regular triangular pyramid can be calculated given the edge of triangular faces. The formula for regular triangular pyramid volume is given as,
Volume = a^{3}/6√2, where 'a' is the edge of the triangular (equilateral) faces.
What Units Are Used With the Volume of the Triangular Pyramid?
The volume of a triangular pyramid is represented in "cubic units". In the metric system of measurement, commonly the units used to express the volume of a triangular pyramid are m^{3}, cm^{3}, in^{3}, milliliters, and liters.
How to Find the Height of a Triangular Pyramid When Given the Volume?
To find the height of a triangular pyramid, given the volume, we can directly apply the following formula, substitute the known values and solve for height:
The volume of Triangular Pyramid = 1/3 × Base Area × Height
⇒ Height of Triangular Pyramid = 3 × Volume/ Base Area
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