102 LearnersLast updated on July 17th, 2025
Volume of Triangular Pyramid
The volume of a triangular pyramid is the total space it occupies or the number of cubic units it can hold. A triangular pyramid is a 3D shape with a triangular base and three triangular faces that meet at a point. To find the volume of a triangular pyramid, we multiply the area of the base by the height of the pyramid and divide by 3. In real life, kids relate to the volume of a triangular pyramid by thinking of objects like tents, roofs, or certain types of cakes. In this topic, let’s learn about the volume of a triangular pyramid.
What is the volume of a triangular pyramid?
The volume of a triangular pyramid is the amount of space it occupies.
It is calculated using the formula: Volume = (Base Area × Height) / 3 Where 'Base Area' is the area of the triangular base and 'Height' is the perpendicular distance from the base to the apex of the pyramid.
Volume of Triangular Pyramid Formula A triangular pyramid has a triangular base and three triangular faces.
To calculate its volume, find the area of the base, multiply it by the height, and then divide by 3.
The formula for the volume of a triangular pyramid is given as follows: Volume = (Base Area × Height) / 3
How to Derive the Volume of a Triangular Pyramid?
To derive the volume of a triangular pyramid, 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 pyramid in general is:
Volume = (Base Area × Height) / 3
For a triangular pyramid, the base is a triangle, so: Base Area = 1/2 × base × height of the triangle
Volume = (1/2 × base of triangle × height of triangle × height of pyramid) / 3
How to find the volume of a triangular pyramid?
The volume of a triangular pyramid is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
First, find the area of the base. Next, find the height of the pyramid.
Finally, multiply the base area by the height of the pyramid and divide by 3 to find the volume.
Let’s take a look at the formula for finding the volume of a triangular pyramid:
Write down the formula Volume = (Base Area × Height) / 3 The base area is the area of the triangle forming the base of the pyramid.
The height of the pyramid is the perpendicular distance from the base to the apex.
Once we know both the base area and the height, substitute those values into the formula to find the volume.
Tips and Tricks for Calculating the Volume of Triangular Pyramid
Remember the formula: The formula for the volume of a triangular pyramid is: Volume = (Base Area × Height) / 3
Break it down: First calculate the area of the triangular base, then multiply by the height of the pyramid, and divide by 3.
Simplify the numbers: If the base or height is a simple number, calculate these first before dividing by 3.
Check for common formulas: Ensure you’re using the correct formula for the area of a triangle and the volume of a pyramid.
Common Mistakes and How to Avoid Them in Volume of Triangular Pyramid
Making mistakes while learning the volume of a triangular pyramid is common.
Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of triangular pyramids.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area.
Surface area involves all the faces of the pyramid, whereas volume is calculated by finding the base area and using the height of the pyramid.
Remember that volume is (Base Area × Height) / 3.
Mistake 2
Confusing Volume with Base Area
Some kids may think of the pyramid’s base area instead of the volume formula.
Volume is the space inside the pyramid, calculated as (Base Area × Height) / 3, not just the area of the base.
Mistake 3
Using the wrong formula for the base area
Some kids use the wrong formula for the area of the base triangle, affecting the volume calculation.
Ensure you use the correct formula for the base area: 1/2 × base × height of the triangle.
Mistake 4
Confusing linear height with slant height
Confusion often occurs between the height of the pyramid (perpendicular height) and the slant height.
Use the perpendicular height for the volume calculation, not the slant height.
Mistake 5
Incorrectly calculating the base area
Some students make errors calculating the base area, leading to an incorrect volume. Double-check calculations for the triangular base area before using it in the volume formula.
Volume of Triangular Pyramid Examples
Problem 1
A triangular pyramid has a base area of 30 cm² and a height of 12 cm. What is its volume?
The volume of the triangular pyramid is 120 cm³.
Explanation
To find the volume of a triangular pyramid, use the formula: V = (Base Area × Height) / 3 Here, the base area is 30 cm² and the height is 12 cm, so: V = (30 × 12) / 3 = 360 / 3 = 120 cm³
Problem 2
A triangular pyramid has a base area of 50 m² and a height of 9 m. Find its volume.
The volume of the triangular pyramid is 150 m³.
Explanation
To find the volume of a triangular pyramid, use the formula: V = (Base Area × Height) / 3 Substitute the base area (50 m²) and height (9 m): V = (50 × 9) / 3 = 450 / 3 = 150 m³
Problem 3
The volume of a triangular pyramid is 200 cm³, and the base area is 40 cm². What is the height of the pyramid?
The height of the pyramid is 15 cm.
Explanation
If you know the volume and base area of the pyramid, and you need to find the height, rearrange the formula: Height = (Volume × 3) / Base Area Height = (200 × 3) / 40 = 600 / 40 = 15 cm
Problem 4
A triangular pyramid has a base area of 24 inches² and a height of 6 inches. Find its volume.
The volume of the triangular pyramid is 48 inches³.
Explanation
Using the formula for volume:
V = (Base Area × Height) / 3 Substitute the base area (24 inches²) and height (6 inches):
V = (24 × 6) / 3 = 144 / 3 = 48 inches³
Problem 5
You have a triangular pyramid-shaped tent with a base area of 16 ft² and a height of 8 ft. How much space (in cubic feet) is inside the tent?
The tent has a volume of 42.67 cubic feet.
Explanation
Using the formula for volume:
V = (Base Area × Height) / 3
Substitute the base area (16 ft²) and height (8 ft):
V = (16 × 8) / 3 = 128 / 3 ≈ 42.67 ft³
FAQs on Volume of Triangular Pyramid
1.Is the volume of a triangular pyramid 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 height?
4.Can the base area be a decimal or fraction?
5.Is the volume of a triangular pyramid the same as the surface area?
Important Glossaries for Volume of Triangular Pyramid
- Base Area: The area of the triangle forming the base of the pyramid.
- Height of Pyramid: The perpendicular distance from the base to the apex of the pyramid.
- Volume: The amount of space enclosed within a 3D object. In the case of a triangular pyramid, the volume is calculated by multiplying the base area by the height and dividing by 3.
- Apex: The highest point where the triangular faces of the pyramid meet.
- Triangular Pyramid: A 3D shape with a triangular base and three triangular faces meeting at the apex.
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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
