103 LearnersLast updated on July 17th, 2025
Volume of Triangular Prism
The volume of a triangular prism is the total space it occupies or the number of cubic units it can hold. A triangular prism is a 3D shape with two triangular bases and three rectangular faces. To find the volume of a triangular prism, we multiply the area of the base triangle by the height (or length) of the prism. In real life, kids relate to the volume of a triangular prism by thinking of objects like tents or Toblerone chocolate bars. In this topic, let’s learn about the volume of the triangular prism.
What is the volume of the triangular prism?
The volume of a triangular prism is the amount of space it occupies.
It is calculated by using the formula: Volume = Base Area × Height Where 'Base Area' is the area of the triangular base, and 'Height' is the length of the prism.
Volume of Triangular Prism Formula A triangular prism is a 3-dimensional shape with two identical triangular bases.
To calculate its volume, you find the area of one of the triangular bases and multiply it by the prism's height (or length).
The formula for the volume of a triangular prism is given as follows: Volume = (1/2 × base × height of triangle) × length
How to Derive the Volume of a Triangular Prism?
To derive the volume of a triangular prism, we use the concept of volume as the total space occupied by a 3D object.
The formula for the volume of a prism is: Volume = Base Area × Height For a triangular prism: Base Area = 1/2 × base × height of triangle The volume of a triangular prism will be, Volume = (1/2 × base × height of triangle) × length
How to find the volume of a triangular prism?
The volume of a triangular prism is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
Find the area of the triangular base first, then multiply by the height of the prism to find the volume.
Let’s take a look at the formula for finding the volume of a triangular prism: Write down the formula Volume = (1/2 × base × height of triangle) × length The base and height are measurements of the triangle, and the length is the distance between the triangular bases.
Once we have these measurements, substitute the values into the formula to find the volume.
Tips and Tricks for Calculating the Volume of a Triangular Prism
Remember the formula: The formula for the volume of a triangular prism is: Volume = (1/2 × base × height of triangle) × length Break it down: The volume is how much space fits inside the prism.
Calculate the area of the triangular base first, then multiply by the prism's length.
Simplify the numbers: If the base, height, or length are simple numbers, it is easy to calculate.
For example, if base = 4, height = 3, and length = 5, then volume = (1/2 × 4 × 3) × 5 = 30.
Check for base area: If you are given the base area and need to find the volume, simply multiply by the length of the prism.
Common Mistakes and How to Avoid Them in Volume of Triangular Prism
Making mistakes while learning the volume of a triangular prism is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of triangular prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area involves adding the areas of all the faces, while volume is calculated by multiplying the base area by the height.
For example, the volume is (1/2 × base × height of triangle) × length, not adding areas of all faces.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the triangle’s perimeter instead of the volume formula.
Volume is the space inside the prism, whereas perimeter refers to the total length around the edges of a 2D shape.
Do not mix them up.
Mistake 3
Using the wrong Formula for different prisms
Some kids use the formula for the volume of a rectangular prism (length × width × height) instead of the triangular prism formula.
Mistake 4
Confusing triangular area with base area
Thinking of volume in terms of linear measurements.
This happens when someone uses the triangle's side length (a linear measurement) instead of calculating the area of the triangle.
Mistake 5
Incorrectly calculating the triangle's area
Some students calculate the given base area incorrectly.
For example, if the triangle's base and height are given, they might forget to multiply by 1/2 to find the base area.
Volume of Triangular Prism Examples
Problem 1
A triangular prism has a triangular base with a base of 4 cm and height of 3 cm, and the length of the prism is 5 cm. What is its volume?
The volume of the triangular prism is 30 cm³.
Explanation
To find the volume of a triangular prism, use the formula: V = (1/2 × base × height of triangle) × length Here, the base = 4 cm, height = 3 cm, and length = 5 cm, so: V = (1/2 × 4 × 3) × 5 = 30 cm³
Problem 2
A triangular prism has a base area of 10 m² and a length of 7 m. Find its volume.
The volume of the triangular prism is 70 m³.
Explanation
To find the volume of a triangular prism, use the formula: V = Base Area × length Substitute the base area and length: V = 10 m² × 7 m = 70 m³
Problem 3
The volume of a triangular prism is 50 cm³. Its base area is 10 cm². What is the length of the prism?
The length of the prism is 5 cm.
Explanation
If you know the volume and base area of the prism, and you need to find the length, you’ll divide the volume by the base area. The formula for the length is: Length = Volume / Base Area = 50 cm³ / 10 cm² = 5 cm
Problem 4
A triangular prism has a triangular base with a base of 5 inches and height of 2 inches, and the length of the prism is 8 inches. Find its volume.
The volume of the triangular prism is 40 inches³.
Explanation
Using the formula for volume: V = (1/2 × base × height of triangle) × length Substitute the base = 5 inches, height = 2 inches, and length = 8 inches: V = (1/2 × 5 × 2) × 8 = 40 inches³
Problem 5
You have a triangular prism with a base area of 15 ft² and a length of 4 ft. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 60 cubic feet.
Explanation
Using the formula for volume: V = Base Area × length Substitute the base area = 15 ft² and length = 4 ft: V = 15 ft² × 4 ft = 60 ft³
FAQs on Volume of Triangular Prism
1.Is the volume of a triangular prism the same as the surface area?
2.How do you find the volume if the base area is given?
3.What if I have the volume and need to find the length?
4.Can the base area or length be a decimal or fraction?
5.Is the volume of a triangular prism the same as the surface area?
Important Glossaries for Volume of Triangular Prism
- Base Area: The area of one of the triangular bases, calculated as 1/2 × base × height of triangle.
- Height of Triangle: The vertical height from the base to the apex of the triangle.
- Length (Height of Prism): The distance between the two triangular bases.
- Volume: The amount of space enclosed within a 3D object, calculated for a triangular prism by multiplying the base area by the length. It is expressed in cubic units (e.g., cm³, m³).
- Cubic Units: The units of measurement used for volume. If the measurements are in centimeters (cm), the volume will be in cubic centimeters (cm³); if in meters, it will be in cubic meters (m³).
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
