116 LearnersLast updated on July 11th, 2025
Volume of Parallelogram Prism
The volume of a parallelogram prism is the total space it occupies or the number of cubic units it can hold. A parallelogram prism is a 3D shape with parallelogram bases. To find the volume of a parallelogram prism, we multiply the base area by its height. In real life, kids relate to the volume of a parallelogram prism by thinking of things like a tent or certain types of aquariums. In this topic, let’s learn about the volume of the parallelogram prism.
What is the volume of the parallelogram prism?
The volume of a parallelogram 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 parallelogram base and the height is the perpendicular distance between the bases.
The formula for the volume of a parallelogram prism is given as follows: Volume = Base Area × Height
How to Derive the Volume of a Parallelogram Prism?
To derive the volume of a parallelogram prism, we use the concept of volume as the total space occupied by a 3D object. The formula for the volume of any prism is: Volume = Base Area × Height
For a parallelogram prism, the base is a parallelogram, and the height is the perpendicular distance between the two parallelogram bases.
Therefore, the volume of a parallelogram prism is calculated as: Volume = Base Area × Height
How to find the volume of a parallelogram prism?
The volume of a parallelogram prism is always expressed in cubic units, for example, cubic centimeters (cm³), cubic meters (m³).
To find the volume, calculate the base area first, and then multiply it by the height.
Let’s take a look at the formula for finding the volume of a parallelogram prism: Write down the formula Volume = Base Area × Height
The base area is the area of the parallelogram base. Once we know the base area and the height, substitute those values into the formula to find the volume.
Tips and Tricks for Calculating the Volume of a Parallelogram Prism
Remember the formula: The formula for the volume of a parallelogram prism is simple: Volume = Base Area × Height
Break it down: The volume is how much space fits inside the prism. Calculate the base area first and then multiply by the height.
Simplify the numbers: If the base area and height values are simple numbers, it is easy to multiply them.
Check for consistent units: Ensure the base area and height are in compatible units before calculating the volume.
Common Mistakes and How to Avoid Them in Volume of Parallelogram Prism
Making mistakes while learning the volume of a parallelogram prism is common. Let’s look at some common mistakes and how to avoid them to get a better understanding of the volume of parallelogram 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 adding the areas of all faces, but volume is calculated by multiplying the base area by the height.
Mistake 2
Confusing Volume with Perimeter
Some kids may think of the prism’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 prisms
Some kids use the formula for the volume of other types of prisms instead of the parallelogram prism formula. Ensure to use Base Area × Height for parallelogram prisms.
Mistake 4
Confusing cubic volume with linear measurements
Thinking of volume in terms of linear measurements. This happens when someone uses linear dimensions without calculating the area first. Volume relates to cubic measurements.
Mistake 5
Incorrectly calculating the base area
Some students might incorrectly calculate the base area of the parallelogram, leading to errors in the volume calculation. Ensure the base area is calculated correctly.
Volume of Parallelogram Prism Examples
Problem 1
A parallelogram prism has a base area of 20 cm² and a height of 10 cm. What is its volume?
The volume of the parallelogram prism is 200 cm³.
Explanation
To find the volume of a parallelogram prism, use the formula: V = Base Area × Height
Here, the base area is 20 cm² and the height is 10 cm, so: V = 20 × 10 = 200 cm³
Problem 2
A parallelogram prism has a base area of 15 m² and a height of 8 m. Find its volume.
The volume of the parallelogram prism is 120 m³.
Explanation
To find the volume of a parallelogram prism, use the formula: V = Base Area × Height
Substitute the base area (15 m²) and height (8 m): V = 15 × 8 = 120 m³
Problem 3
The volume of a parallelogram prism is 150 cm³, and the height is 5 cm. What is the base area of the parallelogram?
The base area of the parallelogram is 30 cm².
Explanation
If you know the volume of the prism and you need to find the base area, use the formula: Base Area = Volume / Height
Here, Volume = 150 cm³ and Height = 5 cm: Base Area = 150 / 5 = 30 cm²
Problem 4
A parallelogram prism has a base area of 12.5 inches² and a height of 4 inches. Find its volume.
The volume of the parallelogram prism is 50 inches³.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area 12.5 inches² and height 4 inches:
V = 12.5 × 4 = 50 inches³
Problem 5
You have a parallelogram prism with a base area of 25 square feet and a height of 3 feet. How much space (in cubic feet) does the prism occupy?
The prism occupies a volume of 75 cubic feet.
Explanation
Using the formula for volume: V = Base Area × Height
Substitute the base area 25 ft² and height 3 ft:
V = 25 × 3 = 75 ft³
FAQs on Volume of Parallelogram Prism
1.Is the volume of a parallelogram 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 area be a decimal or fraction?
5.What units are used for volume?
Important Glossaries for Volume of Parallelogram Prism
- Base Area: The area of the parallelogram base in a prism, crucial for calculating volume.
- Height: The perpendicular distance between the two parallelogram bases of the prism.
- Volume: The amount of space enclosed within a 3D object, calculated as Base Area × Height for a parallelogram prism.
- Cubic Units: The units of measurement used for volume, such as cm³ or m³, depending on the base area and height units.
- Parallelogram Prism: A 3D shape with parallelogram bases and rectangular lateral faces.
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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.
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: She has songs for each table which helps her to remember the tables
