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131 LearnersLast updated on September 5, 2025
Volume of 3D Triangle
The volume of a 3D triangle, also known as 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 triangular base by the height (or length) of the prism. In real life, kids can relate to the volume of a 3D triangle by thinking of things like a tent, a Toblerone chocolate bar, or a roof of a house. In this topic, let’s learn about the volume of the 3D triangle.
What is the volume of a 3D triangle?
The volume of a 3D triangle is the amount of space it occupies. It is calculated by using the formula:
Volume = Base Area × Height Where the base area is the area of the triangular base, and height is the distance between the triangular bases.
Volume of 3D Triangle Formula: A triangular prism is a 3-dimensional shape with two identical triangular bases and three rectangular faces. To calculate its volume, you multiply the area of the triangular base by the height of the prism. The formula for the volume of a triangular prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of a 3D Triangle?
To derive the volume of a 3D triangle, we use the concept of volume as the total space occupied by a 3D object.
The volume can be derived as follows: The formula for the volume of a triangular prism is: Volume = Base Area × Height
To find the base area: Base Area = 1/2 × Base × Height of Triangle
Then, the volume of the triangular prism will be: Volume = (1/2 × Base × Height of Triangle) × Height of Prism
How to find the volume of a 3D triangle?
The volume of a 3D triangle is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³). To find the volume, calculate the area of the triangular base and multiply it by the height of the prism.
Let’s take a look at the formula for finding the volume of a 3D triangle: Write down the formula: Volume = Base Area × Height Calculate the base area of the triangle: Base Area = 1/2 × Base × Height of Triangle Once we know the base area, substitute that value into the formula: Volume = Base Area × Height of Prism
Tips and Tricks for Calculating the Volume of 3D Triangle
Remember the formula: The formula for the volume of a 3D triangle is: Volume = Base Area × Height Break it down: The volume is how much space fits inside the triangular prism, found by multiplying the base area by the height of the prism. Simplify the numbers: If the base and height of the triangle are simple numbers, it becomes easy to calculate the base area, and subsequently the volume. Check units: Ensure all measurements are in the same units before calculating the volume to avoid errors.
Common Mistakes and How to Avoid Them in Volume of 3D Triangle
Making mistakes while learning the volume of a 3D triangle is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of 3D triangles.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area involves calculating the area of all faces of the prism, while volume is calculated by multiplying the base area by the height.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of the triangular base instead of the volume formula. Volume refers to the space within the prism, whereas perimeter is the total length around the edges of a 2D shape.
Mistake 3
Using the wrong Formula for rectangular prisms
Some kids use the formula for the volume of a rectangular prism instead of using the triangular base area for the triangular prism.
Mistake 4
Confusing base area with base length
Thinking of the base area as just the base length. Remember, the base area involves both the base length and the height of the triangle.
Mistake 5
Incorrectly calculating the base area
Some students might calculate the base area incorrectly by forgetting to multiply by 1/2 when finding the area of the triangle.
Volume of 3D Triangle Examples
Problem 1
A triangular prism has a triangular base with a base length of 6 cm and a height of 4 cm. The height of the prism is 10 cm. What is its volume?
The volume of the triangular prism is 120 cm³.
Explanation
To find the volume of a triangular prism, use the formula:
Base Area = 1/2 × Base × Height of Triangle
= 1/2 × 6 × 4 = 12 cm²
Volume = Base Area × Height of Prism
= 12 × 10 = 120 cm³
Problem 2
A triangular prism has a base area of 15 m² and a height of 8 m. Find its volume.
The volume of the triangular prism is 120 m³.
Explanation
To find the volume of a triangular prism, use the formula:
Volume = Base Area × Height of Prism
= 15 × 8 = 120 m³
Problem 3
The volume of a triangular prism is 200 cm³, and its height is 10 cm. What is the base area of the triangular base?
The base area of the triangular base is 20 cm².
Explanation
If you know the volume of the triangular prism, and you need to find the base area, use the formula:
Volume = Base Area × Height of Prism
Base Area = Volume / Height of Prism
= 200 / 10 = 20 cm²
Problem 4
A tent shaped like a triangular prism has a base with a base length of 5 inches and a height of 3 inches. The height of the prism is 7 inches. Find its volume.
The volume of the triangular prism is 52.5 inches³.
Explanation
Using the formula for volume:
Base Area = 1/2 × Base × Height of Triangle
= 1/2 × 5 × 3 = 7.5 inches²
Volume = Base Area × Height of Prism
= 7.5 × 7 = 52.5 inches³
Problem 5
You have a Toblerone chocolate bar shaped like a triangular prism with a base area of 2.5 inches² and a height of 8 inches. How much chocolate (in cubic inches) is available inside the bar?
The Toblerone bar has a volume of 20 cubic inches.
Explanation
Using the formula for volume:
Volume = Base Area × Height of Prism
= 2.5 × 8 = 20 inches³
FAQs on Volume of 3D Triangle
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 and height are given?
3.What if I have the volume and need to find the base area?
4.Can the base of the triangle be a decimal or fraction?
5.Is the volume of a triangular prism the same as the surface area?
Important Glossaries for Volume of 3D Triangle
- Base Area: The area of the triangular base of the prism, calculated by 1/2 × Base × Height of Triangle.
- Volume: The amount of space enclosed within the 3D object, calculated by multiplying the base area by the height of the prism.
- Triangular Prism: A 3D shape with two identical triangular bases and three rectangular faces.
- Height of Prism: The perpendicular distance between the two triangular bases of the prism.
- Cubic Units: The units of measurement used for volume. If the base and height are in centimeters (cm), the volume will be in cubic centimeters (cm³), and 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
