Volume of Triangular Prism
The volume of a triangular prism is the space occupied by it. A prism is a solid object which has identical bases, flat rectangular side faces, and the same crosssection all along its length. There are different types of prisms that are classified and named as per the shape of their base. Some types of prisms are
 triangular prism (a prism whose base is a triangle)
 square prism (a prism whose base is a square)
 rectangular prism (a prism whose base is a rectangle)
 pentagonal prism (a prism whose base is a pentagon)
 hexagonal prism (a prism whose base is a hexagon)
 octagonal prism (a prism whose base is an octagon)
Similarly, there can be many other types of prisms with different polygons as bases. Each side face of any type of prism is a rectangle.
1.  Definition of Triangular Prism 
2.  Volume of Triangular Prism Formula 
3.  How To Calculate the Volume of Triangular Prism? 
4.  FAQs on Volume of Triangular Prism 
Definition of Triangular Prism
A triangular prism is a polyhedron, made up of two triangular bases and three rectangular sides (or) it is a pentahedron (as it has 5 faces altogether) wherein the edges and vertices of the bases are joined with each other via three rectangular sides. By definition, the two triangular bases are parallel and congruent to each other. It has
 2 bases (which are congruent triangles)
 3 side faces (which are congruent rectangles)
 5 total number of faces
 9 edges
 6 corners
The height of the triangular prism is the perpendicular distance between the centers of the two parallel bases.
Volume of Triangular Prism Formula
The volume of a triangular prism is nothing but the space inside it (or) space occupied it. It is measured in cubic units such as cm^{3}, m^{3}, in^{3}, etc. We will see the formulas to calculate the volumes of different types of triangular prisms. The volume of any prism is obtained by multiplying its base area by its height. i.e.,
The volume of a prism = base area × height
We will use this formula to calculate the volume of a triangular prism as well. We know that the base of a triangular prism is a triangle. By applying the above formula to a triangular prism,
The volume of a triangular prism = area of base triangle × height
Here, we can find the area of the base triangle based on its type and the available information. Here are the formulas to find the area of the base triangle.
 If the base triangle is equilateral (in this case, the prism is called equilateral triangular prism) with each side 'a', then its area is, √3a^{2}/4.
 If the base triangle's base 'b' and height 'h' are given, then its area is (1/2) bh.
 If the base triangle is a rightangled triangle (in this case, the prism is called a right triangular prism) with two legs 'b' and 'h' then its area is (1/2) bh.
 If the base triangle is an isosceles triangle with its sides to be 'a', 'a', and 'b' then its area is (b/4) · √(4a^{2}  b^{2})
 If the base triangle is scalene where all three sides 'a', 'b', and 'c' are given, then its area is calculated using √[s(sa)(sb)(sc)] where s = (a + b + c)/2.
Note that you can apply this formula (which is also called Heron's formula) for an isosceles triangle (or) an equilateral triangle as well.
 If the base triangle's two sides 'a' and 'b' and the included angle 'θ' are given, then its area is found using 1/2 ab sin θ.
How To Calculate the Volume of Triangular Prism?
Here are the steps to calculate the volume of a triangular prism. Before that make sure that all measurements are of the same units. You can also see an example followed by the steps.
Step 1: Identify the type of the base triangle and find its area using a suitable formula (as explained in the previous section).
Step 2: Identify its height (Note that this should be the height of the total prism, not the height of the base triangle).
Step 3: Multiply the base area (from step 1) and the height (from step 2) to find the volume.
Example: Calculate the volume of the triangular prism whose height is 15 in and whose base is an equilateral triangle of side 6 in.
Solution:
Step 1: The base triangle is an equilateral triangle with its side to be a = 6. So its area is found using the formula
√3a^{2}/4 ^{ }= √3(6)^{2}/4 = 9√3 square inches.
Step 2: The height of the prism is 15 in.
Step 3: The volume of the given triangular prism = base area × height = 9√3 × 15 = 135√3 cubic inches.
Solved Examples on Volume of Triangular Prism

Example 1: Determine the volume of a triangular prism whose height is 10 in and whose base triangle's base is 7 in and height is 5 in.
Solution:
The base of the base triangle is, b = 7 in, and its height is h = 5 in.
So the base area = (1/2)(bh) = (1/2) (7 × 5) = 35/2 in^{2}.
The height of the prism is, H = 10 in.
Using the volume of triangular prism formula,
The volume of the given triangular prism = base area × height = (35/2) (10) = 175 in^{3}.

Example 2: Find the volume of the following right triangular prism.
Solution:
The base of the base triangle is, b = 14 ft and its height is h = 8 ft.
So the base area = (1/2)(bh) = (1/2) (14 × 8) = 56 square feet.
The height of the prism is, H = 10 ft.
Using the volume of the triangular prism formula,
The volume of the given triangular prism = base area × height = (56) (10) = 560 ft^{3}.
FAQs on Volume of Triangular Prism
What Is the Volume of Triangular Prism?
The volume of a triangular prism is the space inside it. It is calculated by multiplying its base area by its height. The volume of a triangular prism can be expressed in cubic units such as cm^{3}, m^{3}, in^{3}, etc.
What Is the Formula for Finding the Volume of Triangular Prism?
The formula to find the volume of a triangular prism is base area × height where
 base area = area of the base (which is a triangle)
 height = height of the triangular prism (and not the height of the base)
How To Find the Height of a Triangular Prism With the Volume?
The volume of a triangular prism is its base area multiplied by its height. From this, the height of a triangular prism is obtained by dividing its volume by its base area.
How To Find Volume of Triangular Prism With Right Angle?
If the base of a triangular prism is a rightangled triangle of base 'b' and height 'h' and the height of the prism is 'H", then its base area = (1/2) bh. We know that the volume of the prism is base area × height and hence the volume of the prism, in this case, is found using the formula (1/2) bhH.
What Is the Formula To Calculate the Volume of an Equilateral Triangular Prism?
Consider a triangular prism whose height is 'H' and whose base is an equilateral triangle of side 'a'. Then its base area is √3a^{2}/4. We know that the volume of the prism is base area × height and hence the volume of the prism, in this case, is found using the formula √3Ha^{2}/4.
How To Find the Volume of a Triangular Prism With an Angle Given?
Consider a triangular prism whose height is 'H' and 'a' and 'b' are the two sides of its base with an included angle θ. Then its base area is (1/2) ab sin θ. We know that the volume of the prism is base area × height and hence the volume of the prism, in this case, is found using the formula (1/2) ab sin θ × H.