106 LearnersLast updated on August 30, 2025
Surface Area of Parallelogram Prism
A parallelogram prism is a 3-dimensional shape that has parallelogram-shaped bases. The surface area of the parallelogram prism is the total area covered by its outer surfaces. The surface area includes both its lateral surfaces and its bases. In this article, we will learn about the surface area of a parallelogram prism.
What is the Surface Area of a Parallelogram Prism?
The surface area of a parallelogram prism is the total area occupied by the boundary or surface of the prism.
It is measured in square units.
A parallelogram prism is a 3D shape formed by translating a parallelogram along an axis.
It has two identical parallelogram bases and rectangular lateral faces connecting corresponding sides of the bases.
The surface area of a parallelogram prism includes the area of all its faces: the lateral surface area and the base areas.
Surface Area of a Parallelogram Prism Formula
A parallelogram prism has lateral surfaces and two bases, and its surface area includes the areas of these surfaces.
Consider the prism below to see its lateral surface area, base area, height (h), and the dimensions of the parallelogram base.
A parallelogram prism has:
Lateral Surface Area
Total Surface Area
Lateral Surface Area of a Parallelogram Prism
The lateral surface area is the sum of the areas of all the rectangular faces connecting the parallelogram bases. It can be calculated by multiplying the perimeter of the base by the height of the prism.
The formula for the lateral surface area (LSA) of the parallelogram prism is given as:
Lateral Surface Area = Perimeter of base × Height
Here, the perimeter of the base is the sum of all sides of the parallelogram base, and height is the distance between the two bases.
Total Surface Area of a Parallelogram Prism
The total surface area of the parallelogram prism is the sum of the lateral surface area and twice the area of the base. The formula is:
Total Surface Area = Lateral Surface Area + 2 × Base Area
Where the base area is the area of the parallelogram base.
This can be calculated as the product of the base and height of the parallelogram.
Volume of a Parallelogram Prism
The volume of a parallelogram prism measures the space inside it. It is calculated by multiplying the area of the base by the height of the prism.
The volume formula is: Volume = Base Area × Height (cubic units)
Confusion between LSA and TSA
Students sometimes confuse the lateral surface area (LSA) and the total surface area (TSA) of a parallelogram prism.
Remember that LSA includes only the lateral faces, while TSA includes both the lateral faces and the bases.
Mistake 1
Incorrectly calculating the base area
Some students mistake the formula for the base area of the parallelogram. Remember that the area of a parallelogram is calculated as base × height (height of the parallelogram, not the prism).
Mistake 2
Using height instead of slant height
While this is more pertinent to slanted prisms, ensure you are using the correct height when calculating surface areas. The height should be perpendicular to the bases.
Mistake 3
Forgetting to include both base areas in the total surface area
Students often omit one of the base areas when calculating the total surface area. Always multiply the base area by two when adding to the lateral surface area.
Mistake 4
Assuming all parallelogram prisms are rectangular
Some students assume that all parallelogram prisms have rectangular bases. This is incorrect, as a parallelogram prism can have any parallelogram shape as its base, like a rhombus or a rectangle.
Mistake 5
Solved Examples of Surface Area of Parallelogram Prism
Find the lateral surface area of a parallelogram prism with a base perimeter of 20 cm and a height of 12 cm.
LSA = 240 cm²
Problem 1
Given perimeter of base = 20 cm, height = 12 cm. Use the formula: LSA = Perimeter of base × Height = 20 × 12 = 240 cm²
Find the total surface area of a parallelogram prism with a base area of 15 cm², base perimeter of 18 cm, and height of 10 cm.
Explanation
TSA = 270 cm²
Problem 2
Use the formula: TSA = LSA + 2 × Base Area LSA = Perimeter of base × Height = 18 × 10 = 180 cm² TSA = 180 + 2 × 15 = 180 + 30 = 210 cm²
A parallelogram prism has a base area of 24 cm² and a height of 8 cm.
Find the total surface area if the base perimeter is 22 cm.
Explanation
TSA = 260 cm²
Problem 3
Use the LSA formula: LSA = Perimeter of base × Height = 22 × 8 = 176 cm² TSA = LSA + 2 × Base Area = 176 + 2 × 24 = 176 + 48 = 224 cm²
Find the lateral surface area of a parallelogram prism with a base perimeter of 16 cm and a height of 9 cm.
Explanation
LSA = 144 cm²
Problem 4
LSA = Perimeter of base × Height = 16 × 9 = 144 cm²
The base area of a parallelogram prism is 36 cm², and its lateral surface area is 288 cm².
Find the height if the base perimeter is 24 cm.
Explanation
Height = 12 cm
It is the total area that covers the outside of the prism, including the lateral faces and the bases.
1.What are the two types of surface area in a parallelogram prism?
2.What is the difference between the base area and lateral surface area?
3.Do parallelogram prisms always have rectangular bases?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Parallelogram Prism
Students often make mistakes while calculating the surface area of a parallelogram prism, leading to incorrect answers. Below are some common mistakes and ways to avoid them.
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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