105 LearnersLast updated on August 5th, 2025
Surface Area of Square Prism
A square prism, also known as a rectangular prism with a square base, is a 3-dimensional shape that has square bases. The surface area of a square prism is the total area covered by its outer surface. It includes the areas of the four rectangular faces and the two square bases. In this article, we will learn about the surface area of a square prism.
What is the Surface Area of a Square Prism?
The surface area of a square prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
A square prism is a 3D shape with two parallel square bases and four rectangular faces connecting the bases.
The surface area of a square prism includes the area of the four rectangular faces and the two square bases. Square prisms are a type of rectangular prism where the bases are squares.
Surface Area of a Square Prism Formula
A square prism has two types of surface areas: the lateral surface area and the total surface area. Look at the square prism below to see its surface area, height(h), and side length(s) of the square base.
A square prism has two types of surface areas:
- Lateral Surface Area of a Square Prism
- Total Surface Area of a Square Prism
Lateral Surface Area of a Square Prism
The lateral surface area of a square prism is the total area of the four rectangular faces, excluding the base areas.
The formula for the lateral surface area (LSA) of the square prism is given as:
Lateral Surface Area = 4sh square units
Here, s is the side length of the square base. h is the height of the prism.
Total Surface Area of a Square Prism
The total area occupied by the square prism, including the area of the lateral surfaces and the area of the two square bases, is known as the total surface area of the square prism.
The total surface area of a square prism is calculated by using the formula: Total surface area = 2s² + 4sh square units Where s is the side length of the square base. h is the height of the prism.
Derivation of the Total Surface Area of a Square Prism
To find the total surface area of a square prism, consider its two square bases and four rectangular lateral faces.
Total surface area of a square prism = 2 × area of base + lateral surface area
Here, the area of the base = s² Lateral surface area = 4sh
Substituting the formulas into the total surface area, Total surface area of a square prism, T = 2s² + 4sh
Volume of a Square Prism
The volume of a square prism shows how much space is inside it. It tells us how much it can hold. The volume of a square prism can be found by using the formula: Volume = s²h cubic units
Confusion between LSA and TSA
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a square prism are the same. This confusion arises because both involve the side length and the height. Always remember that LSA is only for the lateral faces, and TSA includes both the lateral surfaces and the bases.
Mistake 1
Using incorrect dimensions
Some students mistakenly use incorrect dimensions when finding the lateral surface area. Remember the formula for lateral surface area is 4sh, so always use the correct side length and height.
Mistake 2
Ignoring the bases in total surface area
A common mistake is to calculate only the lateral surface area and forget to add the base areas. Always include both base areas when calculating the total surface area.
Total surface area = lateral surface area + 2 × base area.
Mistake 3
Confusing a square prism with a cube
Some students mistakenly believe that a square prism and a cube are the same because both have square bases.
However, a cube has all sides equal, whereas a square prism has equal square bases but potentially different height. So, use the appropriate formulas.
Mistake 4
Solved Examples of Surface Area of Square Prism
Find the lateral surface area of a square prism with a side length of 5 cm and a height of 10 cm.
LSA = 200 cm²
Problem 1
Given s = 5 cm, h = 10 cm. Use the formula: LSA = 4sh = 4 × 5 × 10 = 20 × 10 = 200 cm²
Find the total surface area of a square prism with side length 4 cm and height 7 cm.
Explanation
TSA = 136 cm²
Problem 2
Use the formula: TSA = 2s² + 4sh = 2 × 4² + 4 × 4 × 7 = 2 × 16 + 112 = 32 + 112 = 144 cm²
A square prism has a side length of 6 cm and a height of 9 cm. Find the total surface area.
Explanation
TSA = 234 cm²
Problem 3
Use the TSA formula: TSA = 2s² + 4sh = 2 × 6² + 4 × 6 × 9 = 2 × 36 + 216 = 72 + 216 = 288 cm²
Find the lateral surface area of a square prism with side length 3.5 cm and height 8 cm.
Explanation
LSA = 112 cm²
Problem 4
LSA = 4sh = 4 × 3.5 × 8 = 14 × 8 = 112 cm²
The height of a square prism is 15 cm, and its lateral surface area is 300 cm². Find the side length.
Explanation
Side length = 5 cm
It is the total area that covers the outside of the square prism, including its lateral surfaces and both bases.
1.What are the two types of surface area in a square prism?
2.What is the difference between lateral surface area and total surface area?
3.Is a square prism the same as a cube?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Square Prism
Students often make mistakes while calculating the surface area of a square prism, which leads to wrong answers. Below are some common mistakes and the 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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