Volume of a Triangular Prism

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.

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.

Read, More:

• Volume of a Cone
• Volume of a Cylinder
• Volume of a Sphere

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

Unsolved Practice Problems - Volume of a Triangular Prism

Problem 1: Find the volume of a triangular prism with a base length of 5 cm, a base height of 8 cm, and a prism height of 10 cm.

Problem 2: Calculate the volume of a triangular prism where the triangular base has a base of 7 m, a height of 3 m, and the prism has a height of 12 m.

Problem 3: A triangular prism has a base area of 15 square inches and a height of 20 inches. What is the volume of the prism?

Problem 4: Determine the volume of a triangular prism with a base length of 6.5 cm, a base height of 4 cm, and a prism height of 9 cm.

Problem 5: Find the volume of a triangular prism where the base triangle has sides of 5 cm, 12 cm, and 13 cm, and the prism height is 10 cm.

Problem 6: Calculate the volume of a triangular prism with an equilateral triangle base of side length 4 m and a prism height of 7 m.

Problem 7: A triangular prism has a base triangle with a base of 9 cm and a height of 6 cm. If the prism height is 15 cm, what is its volume?

Problem 8: Determine the volume of a triangular prism where the base triangle is a right triangle with legs of 8 cm and 15 cm, and the prism height is 20 cm.

Problem 9: Find the volume of a triangular prism with a base triangle having sides of 10 cm, 10 cm, and 12 cm, and a prism height of 18 cm.

Problem 10: A triangular prism has a base area of 50 square feet and a height of 25 feet. What is the volume of the prism?