Volume of an Equilateral Triangular Prism
The volume of an equilateral triangular prism is defined as the total space an object occupies in 3D plane. An equilateral triangular prism is a threedimensional shape having its bases as equilateral triangles. A triangular prism is a prism bounded on the top and bottom by two paralleled triangular bases and bounded on the sides by three rectangular faces. Let's learn how to find the volume of an equilateral triangular prism and its volume in detail here with the help of few solved examples and practice questions.
What Is Volume of an Equilateral Triangular Prism?
Volume of an equilateral triangular prism is defined as the total space occupied by an equilateral prism. The volume of a triangular prism 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. An equilateral triangular prism comprises 2 bases, 3 faces, 9 edges, and 6 corners. Let us see how to find the formula of the volume of an equilateral triangular prism.
Volume of an Equilateral Triangular Prism Formula
The volume of a triangular prism can be easily found out by just knowing the base area and its height. The formula to calculate the volume of any prism is given as, Base Area × Height
Now considering that the base of the triangular prism is an equilateral triangle of side a. The base area of the triangular prism is (√3/4) a^{2}. Thus, the equilateral triangular pyramid volume can be given as :
Volume of equilateral triangular prism, V = (√3/4)a^{2} × h
where,
 a = Side length
 h = Height of the prism
How to Find the Volume of an Equilateral Triangular Prism?
As we learned in the previous section, the volume of an equilateral triangular prism could be found using V = (√3/4)a^{2} × h. Thus, we follow the below steps to find the volume of equilateral triangular prism.
 Step 1: Determine the base area and the height of the prism.
 Step 2: Find the volume using the general formula V = Base Area × Height or V = (√3/4)a^{2} × h, when the side of the equilateral triangle 'a' and the height 'h' of a triangular prism is known.
 Step 3: Represent the final answer with cubic units.
Examples on Volume of an Equilateral Triangular Prism

Example 1: Find the volume of an equilateral triangular prism with a side length measuring 4 units and a height of 5 units.
Solution:
We know that for a triangular prism whose side is 'a', the volume is:
V = (√3/4)a^{2} × h
Substituting 'a' as 4 we get
V = √3 × 4 × 5
Answer: Volume of the triangular prism is 20√3 units^{3}

Example 2: What is the volume of an equilateral triangular prism 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 prism = Base Area × HeightPutting the values in the formula: 9 × 4 = 36 in^{3}
Answer: The volume of the given triangular prism is 36 in^{3}.
Practice Questions on Volume of an Equilateral Triangular Prism
FAQs on Volume of an Equilateral Triangular Prism
What Is Meant By Volume of Triangular Prism?
Volume of the equilateral prism is defined as the total space it covers inside itself. An equilateral triangular prism is a threedimensional shape having its bases as equilateral triangles.
How Do You Find the Volume of an Equilateral Triangular Prism?
The volume of an equilateral triangular prism can be easily found out by using the formula, Volume = (√3/4)a^{2} × h, where,'a' is side length and 'h' is the height of the equilateral triangular prism.
What Units Are Used With the Volume of the Triangular Prism?
In the metric system of measurement, volume of an equilateral triangular prism is expressed in cubic units, like m^{3}, in^{3}, cm^{3}, ft^{3}, yd^{3}, etc. Other common units of volume are milliliters and liters.
What Is Volume of an Equilateral Triangular Prism Formula?
The volume of an equilateral triangular prism formula is used to calculate the volume when the side length and height of the equilateral prism are given. The formula is given as,
Volume = (√3/4)a^{2} × h
where,
 'a' = Side length, and,
 'h' = Height of equilateral triangular prism.
How to Find the Height When Given the Volume of an Equilateral Triangular Prism?
To find the height of equilateral triangular pyramid, given the volume, we can directly apply the following formula, substitute the known values and solve for height:
Volume of Equilateral Triangular Pyramid, V = (√3/4)a^{2} × h
⇒ Height of Triangular Pyramid, h = (4 × V)/((√3 × a^{2})
where,
 V = Volume of equilateral prism
 a = Side length, and,
 h = Height of equilateral triangular prism.
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