Topics
Integers
- Natural Numbers
- Whole Numbers
- Negative and Positive Numbers
- Integers
- Representation of Integers on the Number Line
- Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Closure Property of Multiplication of Integers
- Commutative Property of Multiplication of Integers
- Multiplication of Integers with Zero
- Multiplicative Identity of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Making Multiplication Easier of Integers
- Division of Integers
- Properties of Division of Integers
Fractions and Decimals
- Concept of Fraction
- Types of Fractions
- Concept of Proper and Improper Fractions
- Concept of Mixed Fractions
- Concept of Equivalent Fractions
- Like and Unlike Fraction
- Comparing Fractions
- Addition of Fraction
- Subtraction of Fraction
- Multiplication of a Fraction by a Whole Number
- Using Operator 'Of' with Multiplication and Division
- Multiplication of Fraction
- Division of Fractions
- Concept of Reciprocals or Multiplicative Inverses
- Problems Based on Fraction
- The Decimal Number System
- Comparing Decimal Numbers
- Addition of Decimal Fraction
- Subtraction of Decimal Numbers
- Multiplication of Decimal Numbers
- Division of Decimal Numbers
- Problems Based on Decimal Numbers
Data Handling
Simple Equations
Lines and Angles
The Triangle and Its Properties
- Basic Concepts of Triangles
- Classification of Triangles based on Sides
- Classification of Triangles based on Angles
- Median of a Triangle
- Altitudes of a Triangle
- Exterior Angle of a Triangle and Its Property
- Some Special Types of Triangles - Equilateral and Isosceles Triangles
- Basic Properties of a Triangle
- Right-angled Triangles and Pythagoras Property
Comparing Quantities
- Ratio
- Concept of Equivalent Ratios
- Proportion
- Unitary Method
- Basic Concept of Percentage
- Estimation in Percentages
- Interpreting Percentages
- Conversion between Percentage and Fraction or Decimal
- Ratios to Percents
- Increase Or Decrease as Percent
- Basic Concepts of Profit and Loss
- Profit or Loss as a Percentage
- Calculation of Interest
Congruence of Triangles
- Similarity and Congruency of Figures
- Congruence Among Line Segments
- Congruence of Angles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- Criteria for Similarity of Triangles
- SAS Congruence Criterion
- ASA Congruence Criterion
- RHS Congruence Criterion
- Exceptional Criteria for Congruence of Triangles
Rational Numbers
- Rational Numbers
- Equivalent Rational Number
- Positive and Negative Rational Numbers
- Rational Numbers on a Number Line
- Rational Numbers in Standard Form
- Comparison of Rational Numbers
- Rational Numbers Between Two Rational Numbers
- Addition of Rational Number
- Subtraction of Rational Number
- Multiplication of Rational Numbers
- Division of Rational Numbers
Perimeter and Area
- Basic Concepts in Mensuration
- Concept of Perimeter
- Perimeter of a Rectangle
- Perimeter of Squares
- Perimeter of Triangle
- Perimeter of Polygon
- Concept of Area
- Area of Square
- Area of Rectangle
- Triangles as Parts of Rectangles and Square
- Generalising for Other Congruent Parts of Rectangles
- Area of a Parallelogram
- Area of a Triangle
- Circumference of a Circle
- Area of Circle
- Conversion of Units
- Problems based on Perimeter
- Problems based on Area
Practical Geometry
- Construction of a Line Parallel to a Given Line, Through a Point Not on the Line
- Construction of Triangles
- Constructing a Triangle When the Length of Its Three Sides Are Known (SSS Criterion)
- Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them Are Known. (SAS Criterion)
- Constructing a Triangle When the Measures of Two of Its Angles and the Length of the Side Included Between Them is Given. (ASA Criterion)
- Constructing a Right-angled Triangle When the Length of One Leg and Its Hypotenuse Are Given (RHS Criterion)
Algebraic Expressions
Exponents and Powers
- Concept of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Numbers with Exponent Zero, One, Negative Exponents
- Miscellaneous Examples Using the Laws of Exponents
- Decimal Number System Using Exponents and Powers
- Crores
Symmetry
Visualizing Solid Shapes
- Introduction
- Formula: Perimeter of Squares
- Example 1
- Example 2
- Key Points Summary
Introduction
Perimeter is simply the distance you walk if you go around the boundary (or outside) of a shape—like walking along the border of a park or tracing your finger around a square. In this topic, we'll focus on squares, which have special properties that make calculating their perimeter super easy!
Formula: Perimeter of Squares
Perimeter of Square = Total boundary of the square
= Side + Side + Side + Side
P = 4 × Side
Or: P = 4s (where 's' represents the side length)
side = ` "perimeter"/"4"`
Always include the correct linear unit (cm, m, mm, km, etc.)
Example 1
Find perimeter
Perimeter of the Square = Sum of the lengths of its four sides.
= AB + BC + CD + DA
= AB + AB + AB + AB.... (All four sides of the square are equal.)
= 4 × AB
= 1m + 1 m + 1 m + 1 m
= 4 × 1 m
= 4 m
Example 2
A square photo frame has a perimeter of 32 inches. What is the length of one side?
Solution:
-
Perimeter (P) = 32 inches
-
Formula: P = 4 × s
-
Therefore: s = P ÷ 4
-
s = 32 ÷ 4 = 8 inches
-
Answer: Each side is 8 inches
Why this works: If the perimeter is the total of all 4 sides, and all sides are equal, then dividing the perimeter by 4 gives us one side.
Key Points Summary
| Concept | Explanation |
|---|---|
| Square | A 4-sided shape with all sides equal and all angles 90° |
| Perimeter | Total distance around the boundary of a shape |
| Formula | P = 4 × side (or P = 4s) |
| Units | Always use linear units (cm, m, mm, km, etc.) |
| Key Property | All 4 sides of a square are equal |
| Reverse Calculation | Side = Perimeter ÷ 4 |
Example Question 1
Pinky runs around a square field of side 75 m, Bob runs around a rectangular field with length 160 m and breadth105 m. Who covers more distance and by how much?
Distance covered by Pinky in one round = Perimeter of the square
= 4 × length of a side
= 4 × 75 m
= 300 m
Distance covered by Bob in one round = Perimeter of the rectangle
= 2 × (length + breadth)
= 2 × (160 m + 105 m)
= 2 × 265 m
= 530 m
Difference in the distance covered = 530 m – 300 m = 230m.
Therefore, Bob covers more distance by 230 m.
Example Question 2
The perimeter of a rectangle of length 28 cm and breadth 20 cm is equal to the perimeter of a square. What is the length of the side of that square?
Perimeter of rectangle = 2 (length + breadth)
= 2 (28 + 20)
= 96
If the side of that square is a then 4a = 96
Perimeter of square = 96
4a = 96
∴ a = = `96/4` = 24.
Side of the square is 24 cm.
