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103 LearnersLast updated on September 4, 2025
Surface Area of Square
A square is a 2-dimensional shape with four equal sides and four right angles. The surface area of a square is the total area covered by its surface. It is measured in square units. In this article, we will learn about the surface area of a square.
What is the Surface Area of a Square?
The surface area of a square is the total area occupied by its boundary or surface. It is measured in square units.
A square is a 2D shape with four equal sides and four right angles.
Since all sides of a square are equal, calculating the surface area involves squaring the length of one side.
Surface Area of a Square Formula
A square has a simple formula for calculating its surface area. Look at the square below to see its side length (s).
The formula for the surface area of a square is: Surface Area of a Square = s² square units
Understanding the Surface Area of a Square
The area of a square can be visualized as the amount of space enclosed within its four sides.
Since a square has four equal sides, its area is calculated by multiplying the side length by itself. This is why the formula is s². Here, s is the length of one side of the square.
Examples of Surface Area of a Square
To understand how to calculate the surface area of a square, consider the following examples.
Applications of Surface Area of a Square
The surface area of a square is used in various real-life applications, such as calculating the area required for flooring, painting, or any task involving square-shaped surfaces. Knowing how to compute the area of a square is a fundamental skill in geometry and practical tasks.
Common Mistakes in Surface Area of a Square
While calculating the surface area of a square is straightforward, there are common mistakes that people make. Below are some common errors and how to avoid them.
Confusion between Perimeter and Surface Area
Students sometimes confuse the perimeter (the total distance around the square) with the surface area. Remember that the perimeter is 4 times the side length, while the surface area is the side length squared.
Mistake 1
Incorrect Formula Application
Some students mistakenly use the formula for the area of other shapes, such as rectangles. Always ensure you use the correct formula: s² for squares.
Mistake 2
Neglecting Units
A common mistake is neglecting to include units in the final answer. Always remember to specify that the surface area is in square units (e.g., cm², m²).
Mistake 3
Misidentifying the Side Length
Students often misidentify the side length, especially when given diagonal measurements. Ensure you know which measurement represents the side of the square.
Mistake 4
Assuming All Quadrilaterals Have the Same Formula
Some students assume that all quadrilaterals, such as rectangles and rhombuses, have the same area formula. Remember that a square has its own unique formula due to its equal sides.
Mistake 5
Solved Examples of Surface Area of Square
Find the surface area of a square with a side length of 5 cm.
Surface Area = 25 cm²
Problem 1
Given s = 5 cm. Use the formula: Surface Area = s² = 5 × 5 = 25 cm²
Calculate the surface area of a square with a side length of 10 m.
Explanation
Surface Area = 100 m²
Problem 2
Use the formula: Surface Area = s² = 10 × 10 = 100 m²
A square garden has a side length of 12 m. What is its surface area?
Explanation
Surface Area = 144 m²
Problem 3
Given s = 12 m. Use the formula: Surface Area = s² = 12 × 12 = 144 m²
Find the surface area of a square plot with a side length of 8.5 m.
Explanation
Surface Area = 72.25 m²
Problem 4
Surface Area = s² = 8.5 × 8.5 = 72.25 m²
The side length of a square is 7 cm. Calculate its surface area.
Explanation
Surface Area = 49 cm²
It is the total area covered by the square, calculated as the square of its side length.
1.Is surface area of a square the same as its area?
2.What is the formula for the surface area of a square?
3.Can the surface area be negative?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in the Surface Area of a Square
Students often make mistakes while calculating the surface area of a square, which leads to incorrect results. 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.
Fun Fact
: She has songs for each table which helps her to remember the tables
