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Volume of a Triangular Prism

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A triangular prism is a 3-D prism made up of a triangular base. It is defined as a three-dimensional solid shape with flat sides and equal bases. It has no bases and faces that are either parallelograms or rectangles. Three rectangular planes and two parallel triangle bases make up a triangular prism. Let’s learn about the volume of a Triangular Prism, its formula, and others in detail.

Triangular Prism

 

What is the Volume of a Triangular Prism?

Volume of the triangular prism is the space occupied by it in 3 dimensions. It is calculated by multiplying the base area of the triangle by its length. the volume of a triangular prism is measured in unit3, cm3, m3, and others.  The formula for the Volume of a Triangular Prism can easily be understood if we know about a triangular prism. Now learning about Triangular Prism,

Triangular Prism Definition

A triangular prism is a polyhedron with 2 triangular parallel bases and three rectangular side faces. A triangular prism has,

  • 2 Triangular Bases
  • 3 Rectangular Side Faces
  • 9 Edges
  • 6 Vertices

Volume of Triangular Prism Formula

The volume of a triangular prism is defined as the amount of space it takes. In other words, the enclosed area or region of the prism is called its volume. To calculate the volume of a triangular prism, the values of its base area and length are required. Its formula equals the product of base area and length. Its unit of measurement is cubic meters (m3).

V = B × l

where,
V is the volume,
B is the base area,
l is the length of prism.

The formula for the base area of a triangular prism is given by,

B = 1/2 × b × h

where,
B is the base area,
b is the triangular base,
h is the height of prism.

How to find the Volume of a Triangular Prism?

Let’s take an example to understand how we can calculate the volume of a triangular prism.

Example: Calculate the volume of a triangular prism with a base area of 100 sq. m and a length of 3 m.

Solution:

Step 1: Note the base area and length of the triangular prism. In this example, the base area of the prism is 100 sq. m and length is 3 m.

Step 2: We know that the volume of a triangular prism is equal to B × l. Substitute the given value of base area and length in the formula.

Step 3: So, the volume of triangular prism is calculated as, V = 100 × 3 = 300 cu. m.

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Solved Example on Volume of Triangular Prism

Example 1: Calculate the volume of a triangular prism with a triangular base length of 8 m and triangular base height of 15 m and a length of 4 m.

Solution:

We have, For triangular base,

b = 8 m, h = 15 cm

Area of base(B) = 1/2 × b × h
                         = 1/2 × 8 × 15
                         = 60

l = 4

Using the formula we get,

V = B × l
   = 60 × 4
   = 240 cu. m

Example 2: Calculate the volume of a triangular prism with a base area of 30 sq. m and a length of 2 m.

Solution:

We have,

B = 30

l = 2

Using the formula we get,

V = B × l

   = 30 × 2

   = 60 cu. m

Example 3: Calculate the base area of a triangular prism if its volume is 350 cu. m and length are 7 m.

Solution:

We have,

V = 350
l = 7

Using the formula we get,

V = B × l

B = V/l

B = 350/7

B = 50 sq. m

Example 4: Calculate the length of a triangular prism if its volume is 400 cu. m and the base area is 150 sq. m.

Solution:

We have,

V = 400
B = 150

Using the formula we get,

V = B × l

l = V/B

l = 400/150

l = 2.67 m

Example 5: Calculate the volume of a triangular prism if its base is 7 m, height is 10 m and length is 8 m.

Solution:

We have, 

b = 7
h = 10
l = 8

Using the formula we have,

V = B × l

   = 1/2 × b × h × l

   = 1/2 × 7 × 10 × 8

   = 7 × 5 × 12

   = 420 cu. m

FAQs on Volume of Triangular Prism

Question 1: What is the volume of a triangular prism?

Answer:

The volume of a triangular prism is the space occupied by the triangular prism. It can also be comprehended as the total liquid that a prism can hold. It is measured in cubic units, m3, cm3.

Question 2: What is the formula for finding the volume of a triangular prism?

Answer:

Formula for finding the volume of a Triangular Prism, 

Volume = B× L

where,
B is the Area of triangular base
L is the length of triangular prism

Question 3: How many Faces does a Triangular Prism have?

Answer:

A triangular prism has 5 faces

  • 2 Triangular Bases
  • 3 Rectangular Side Face

Question 4: How to find the Height of a Triangular Prism with its Volume?

Answer:

Formula for finding the volume of a Triangular Prism, 

Volume = B× L

where,
B is the Area of triangular base
L is the length of triangular prism

Now, the length of triangular prism can be called the height of triangular prism so its height can be calculated by dividing its volume by its base area.



Last Updated : 11 Jan, 2024
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