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142 LearnersLast updated on December 11, 2025
Volume of Trapezoidal Prism
The volume of a trapezoidal prism is the total space it occupies or the number of cubic units it can hold. A trapezoidal prism is a 3D shape with two parallel trapezoidal bases and rectangular lateral faces. To find the volume of a trapezoidal prism, we multiply the area of its base by its height. In real life, kids might relate to the volume of a trapezoidal prism by thinking of objects like a tent, a wedge-shaped cheese block, or a roof section. In this topic, letโs learn about the volume of a trapezoidal prism.
What is the volume of the trapezoidal prism?
The volume of a trapezoidal 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 trapezoidal base.
Volume of Trapezoidal Prism Formula: A trapezoidal prism is a 3-dimensional shape with trapezoid bases.
To calculate its volume, first find the area of the trapezoid base and then multiply it by the height of the prism.
The formula for the volume of a trapezoidal prism is given as follows:
Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
How to Derive the Volume of a Trapezoidal Prism?
To derive the volume of a trapezoidal prism, 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 any prism is: Volume = Base Area × Height For a trapezoidal prism: Base Area = 1/2 × (Base1 + Base2) × Height of Trapezoid
The volume of the trapezoidal prism will be, Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
How to find the volume of a trapezoidal prism?
The volume of a trapezoidal prism is always expressed in cubic units, for example, cubic centimeters cm³, cubic meters m³. Calculate the area of the trapezoid base, and multiply it by the prism's height to find the volume.
Let’s take a look at the formula for finding the volume of a trapezoidal prism: Write down the formula Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
First, calculate the area of the trapezoid base using the formula:
Base Area = 1/2 × (Base1 + Base2) × Height of Trapezoid
Then multiply this area by the height of the prism to get the volume.
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Tips and Tricks for Calculating the Volume of a Trapezoidal Prism
Remember the formula: The formula for the volume of a trapezoidal prism is: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
Break it down: Calculate the area of the trapezoidal base first, and then multiply it by the height of the prism.
Simplify the numbers: If the dimensions are simple numbers like 2, 3, or 4, it makes the calculations easier.
Check for correct base dimensions: Always ensure you correctly identify Base1, Base2, and the height of the trapezoid.
Common Mistakes and How to Avoid Them in Volume of Trapezoidal Prism
Making mistakes while learning the volume of a trapezoidal prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of trapezoidal prisms.
Mistake 1
Confusing Volume with Surface Area
Some students confuse the formula for volume with the formula for surface area. Surface area is calculated by summing the areas of all faces, but volume is calculated by finding the area of the base and multiplying it by the height of the prism.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the perimeter of the trapezoidal base 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.
Mistake 3
Using the Wrong Formula for Rectangular Prisms
Some kids use the formula for the volume of a rectangular prism (length × width × height) instead of the trapezoidal prism formula.
Mistake 4
Confusing Base Area with Total Volume
Mistaking the area of the trapezoidal base for the volume of the prism. The base area is only part of the calculation for volume.
Mistake 5
Incorrectly Calculating Base Area
Some students calculate the base area incorrectly by either using wrong base lengths or incorrect height of trapezoid.
Volume of Trapezoidal Prism Examples
Problem 1
A trapezoidal prism has base1 = 3 cm, base2 = 5 cm, height of trapezoid = 4 cm, and height of prism = 10 cm. What is its volume?
The volume of the trapezoidal prism is 160 cm³.
Explanation
To find the volume of a trapezoidal prism, use the formula: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
Here, Base1 = 3 cm, Base2 = 5 cm, Height of Trapezoid = 4 cm, Height of Prism = 10 cm,
so: Volume = (1/2 × (3 + 5) × 4) × 10 = (1/2 × 8 × 4) × 10 = 16 × 10 = 160 cm³
Problem 2
A trapezoidal prism has base1 = 6 m, base2 = 9 m, height of trapezoid = 3 m, and height of prism = 12 m. Find its volume.
The volume of the trapezoidal prism is 270 m³.
Explanation
To find the volume of a trapezoidal prism, use the formula: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
Substitute the values: Volume = (1/2 × (6 + 9) × 3) × 12 = (1/2 × 15 × 3) × 12 = 22.5 × 12 = 270 m³
Problem 3
The volume of a trapezoidal prism is 360 cmยณ. If base1 = 4 cm, base2 = 6 cm, and height of trapezoid = 3 cm, what is the height of the prism?
The height of the prism is 12 cm.
Explanation
If you know the volume of the trapezoidal prism and need to find the height of the prism, use the formula: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
360 = (1/2 × (4 + 6) × 3) × Height of Prism
360 = (1/2 × 10 × 3) × Height of Prism
360 = 15 × Height of Prism
Height of Prism = 360 / 15 = 12 cm
Problem 4
A trapezoidal prism has base1 = 7 inches, base2 = 10 inches, height of trapezoid = 2 inches, and height of prism = 5 inches. Find its volume.
The volume of the trapezoidal prism is 170 inches³.
Explanation
Using the formula for volume: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
Substitute the values: Volume = (1/2 × (7 + 10) × 2) × 5 = (1/2 × 17 × 2) × 5 = 17 × 5 = 85 × 2 = 170 inches³
Problem 5
You have a trapezoidal prism with base1 = 2 feet, base2 = 4 feet, height of trapezoid = 3 feet, and height of prism = 6 feet. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 108 cubic feet.
Explanation
Using the formula for volume: Volume = (1/2 × (Base1 + Base2) × Height of Trapezoid) × Height of Prism
Substitute the values: Volume = (1/2 × (2 + 4) × 3) × 6 = (1/2 × 6 × 3) × 6 = 9 × 6 = 54 × 2 = 108 ft³
FAQs on Volume of Trapezoidal Prism
1.Is the volume of a trapezoidal prism the same as the surface area?
2.How do you find the volume if the base dimensions and height are given?
3.Can the base or height dimensions be decimals or fractions?
4.What if I have the volume and need to find the height of the prism?
5.Are there any real-life examples of trapezoidal prisms?
Important Glossaries for Volume of Trapezoidal Prism
- Base1: One of the parallel sides of the trapezoidal base.
- Base2: The other parallel side of the trapezoidal base.
- Height of Trapezoid: The perpendicular distance between Base1 and Base2.
- Height of Prism: The distance between the two trapezoidal bases.
- Volume: The amount of space enclosed within a 3D object, calculated by the formula for the given shape. In the case of a trapezoidal prism, it is expressed in cubic units (e.g., cm³, m³).
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
