119 LearnersLast updated on July 21st, 2025
Volume of Trapezoid
The volume of a trapezoid is a concept often misunderstood because a trapezoid is typically a 2D shape. However, if we think of a trapezoid as part of a 3D shape like a trapezoidal prism, we can calculate the volume. In such cases, the volume is the total space it occupies or the number of cubic units it can hold. In this topic, let’s 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 using the formula: Volume = Base Area × Height Where the base area is the area of the trapezoid that forms the base of the prism.
The formula for the area of a trapezoid is: Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Volume of Trapezoidal Prism Formula A trapezoidal prism is a 3-dimensional shape with two parallel trapezoidal bases.
To calculate its volume, you multiply the base area by the height (the perpendicular distance between the two bases) of the 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 the trapezoid
The volume of a trapezoidal prism will be, Volume = Base Area × Height of the 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 base area first, then multiply it by the height of the prism 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 = Base Area × Height Calculate the base area using: Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid
Once you have the base area, substitute that value in the formula Volume = Base Area × Height of the prism to find the volume.
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 = Base Area × Height of the prism Break it down: The volume is how much space fits inside the prism.
Calculate the base area of the trapezoid first, then multiply it by the height of the prism.
Simplify the numbers: If the base lengths and height are simple numbers, it is easier to compute the base area.
Check calculations: Ensure you substitute the correct values for Base1, Base2, and the heights when calculating the base area and volume.
Common Mistakes and How to Avoid Them in Volume of Trapezoidal Prism
Making mistakes while learning the volume of trapezoidal prisms 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 the sum of the areas of all faces, but volume is calculated by multiplying the base area by the height of the prism.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the trapezoid’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 other prisms (like rectangular prisms) instead of the trapezoidal prism formula.
Mistake 4
Ignoring the Trapezoid's Height
Some students forget to include the height of the trapezoid when calculating the base area, leading to incorrect volume calculations.
Mistake 5
Incorrectly calculating the base area
Some students make errors in calculating the base area. Ensure you accurately compute (1/2) × (Base1 + Base2) × Height of the trapezoid.
Volume of Trapezoidal Prism Examples
Problem 1
A trapezoidal prism has bases of 4 cm and 6 cm, a height of the trapezoid of 3 cm, and a height of the prism of 10 cm. What is its volume?
The volume of the trapezoidal prism is 150 cm³.
Explanation
To find the volume of a trapezoidal prism, use the formula: Volume = Base Area × Height Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Base Area = (1/2) × (4 + 6) × 3 = 15 cm² Volume = 15 × 10 = 150 cm³
Problem 2
A trapezoidal prism has bases of 8 m and 12 m, a height of the trapezoid of 5 m, and a height of the prism of 7 m. Find its volume.
The volume of the trapezoidal prism is 700 m³.
Explanation
To find the volume of a trapezoidal prism, use the formula: Volume = Base Area × Height Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Base Area = (1/2) × (8 + 12) × 5 = 50 m² Volume = 50 × 7 = 350 m³
Problem 3
The volume of a trapezoidal prism is 500 cm³. The bases of the trapezoid are 5 cm and 7 cm, and the height of the trapezoid is 5 cm. What is the height of the prism?
The height of the prism is 10 cm.
Explanation
If you know the volume of the trapezoidal prism and need to find the height, rearrange the volume formula: Volume = Base Area × Height Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Base Area = (1/2) × (5 + 7) × 5 = 30 cm² Height of the prism = Volume / Base Area = 500 / 30 = 10 cm
Problem 4
A trapezoidal prism has bases of 3 inches and 5 inches, a height of the trapezoid of 4 inches, and a height of the prism of 8 inches. Find its volume.
The volume of the trapezoidal prism is 128 inches³.
Explanation
Using the formula for volume: Volume = Base Area × Height Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Base Area = (1/2) × (3 + 5) × 4 = 16 inches² Volume = 16 × 8 = 128 inches³
Problem 5
You have a trapezoidal prism with bases of 6 feet and 10 feet, a height of the trapezoid of 4 feet, and a height of the prism of 5 feet. How much space (in cubic feet) is available inside the prism?
The prism has a volume of 320 cubic feet.
Explanation
Using the formula for volume: Volume = Base Area × Height Base Area = (1/2) × (Base1 + Base2) × Height of the trapezoid Base Area = (1/2) × (6 + 10) × 4 = 32 feet² Volume = 32 × 5 = 160 ft³
FAQs on Volume of Trapezoidal Prism
1.Is the volume of a trapezoidal prism the same as 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 height of the prism?
4.Can the base lengths be decimals or fractions?
5.Is the volume of a trapezoidal prism the same as surface area?
Important Glossaries for Volume of Trapezoidal Prism
- Base1 and Base2: The lengths of the two parallel sides of the trapezoid.
- Height of the trapezoid: The perpendicular distance between the two bases of the trapezoid.
- Base Area: The area of the trapezoidal base, calculated using (1/2) × (Base1 + Base2) × Height of the trapezoid.
- Height of the prism: The perpendicular distance between the two trapezoidal bases of the prism.
- Volume: The amount of space enclosed within a 3D object, calculated by multiplying the base area by the height of the 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
