102 LearnersLast updated on August 13th, 2025
Properties of Square
A square is a type of quadrilateral that has a lot of unique properties. These properties help students simplify geometric problems related to squares. The properties of a square are: it has four equal sides and four right angles, and the diagonals of the square bisect each other and are equal in length. These properties help students to analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a square.
What are the Properties of a Square?
The properties of a square are simple, and they help students to understand and work with this type of quadrilateral. These properties are derived from the principles of geometry. There are several properties of a square and some of them are mentioned below: Property 1: Four Equal Sides A square has four sides that are equal in length. Property 2: Four Right Angles Each corner of a square forms a right angle. Property 3: Diagonals The diagonals of the square are equal in length and bisect each other at right angles. Property 4: Symmetry A square has four lines of symmetry. Property 5: Area Formula The formula used to calculate the area of the square is given below: Area = side² Here, the length of a side is represented as 'side'.
Tips and Tricks for Properties of a Square
Students tend to confuse and make mistakes while learning the properties of a square. To avoid such confusion, we can follow the following tips and tricks: Four Equal Sides: Students should remember that in a square, all four sides are equal in length. To verify this, students can draw a square and measure each side to see that they are all equal. Diagonals are Equal: Students should remember that in a square, the diagonals are equal in length and intersect at right angles. Right Angles: Students should remember that each angle in a square is a right angle, measuring 90 degrees.
Confusing a Square with a Rectangle
Students should remember that a square has all sides equal in length. Whereas, in a rectangle, opposite sides are equal.
Mistake 1
Misinterpreting the Diagonal Relationship
Students should know and remember that the diagonals of a square are equal and bisect each other at right angles.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice the formula used to find the area of a square, which is given below. The students must also understand the representation of 'side'. Area = side²
Mistake 3
Misunderstanding Angle Relationships
Students should remember that all four angles in a square are right angles, each measuring 90 degrees.
Mistake 4
Forgetting the Equal Side Rule
Students must remember that a square must have all four sides equal in length.
Mistake 5
Solved Examples on the Properties of Squares
In a square, if one side is 5 cm, what is the length of the other sides?
Each side is 5 cm.
Problem 1
In a square, all sides are equal in length. Hence, each side measures 5 cm.
In a square, each angle is what degree?
Explanation
Each angle is 90 degrees.
Problem 2
In a square, students should know that all angles are right angles. Hence, each angle is 90 degrees.
The diagonals of a square intersect at a point O. If angle AOB = 90 degrees, what can you conclude about the diagonals of the square?
Explanation
Diagonals of the square are perpendicular to each other.
Problem 3
The angle AOB is 90 degrees. According to a property of squares, the diagonals of a square are perpendicular to each other.
In square ABCD, if diagonal AC is 8 cm, what is the length of diagonal BD?
Explanation
BD = 8 cm
Problem 4
Since the diagonals of a square are equal, if AC = 8 cm, then BD = AC = 8 cm.
A square has a side length of 6 cm. What is the area of the square?
Explanation
Area = 36 sq cm.
A square is a quadrilateral that has four equal sides and four right angles.
1.How many pairs of equal sides does a square have?
2.Are all sides of a square equal?
3.How do you find the area of a square?
4.Can a square have unequal sides?
Common Mistakes and How to Avoid Them in Properties of Squares
Students tend to get confused when understanding the properties of a square, and they tend to make mistakes while solving problems related to these properties. Here are some common mistakes students tend to make and the solutions to said common mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
