Surface Area of Parallelogram Prism
2026-02-28 11:48 Diff
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Last updated on August 30, 2025

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.

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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.

Problem 1

Given perimeter of base = 20 cm, height = 12 cm. Use the formula: LSA = Perimeter of base × Height = 20 × 12 = 240 cm²

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

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

Okay, lets begin

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

Well explained 👍

Problem 4

LSA = Perimeter of base × Height = 16 × 9 = 144 cm²

Okay, lets begin

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

Well explained 👍

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?

Lateral surface area and total surface area are the two types of surface area.

2.What is the difference between the base area and lateral surface area?

Base area is the area of the parallelogram base, while lateral surface area is the sum of the areas of the rectangular faces.

3.Do parallelogram prisms always have rectangular bases?

No, parallelogram prisms can have any parallelogram shape as their base.

4.What unit is surface area measured in?

Surface area is always measured in square units like cm², m², or in².

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.

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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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