Course Content
Chapter 1 Rational Numbers
0/5
Introduction
Properties of Rational Numbers
Role of 0 and 1
Distributivity of multiplication over addition for rational numbers
Additive Inverse and Multiplicative Inverse
Chapter 2 Linear Equations in one variable
0/3
Algebraic Expressions and Equations
Solving Equations having the Variable on both Sides
Reducing Equations to Simpler Form
Chapter 3 Understanding Quadrilaterals
0/7
Plane Surface and Plane Curve
Polygons and Their Types
Sum of the Measures of the Exterior Angles of a Polygon
Kinds of Quadrilaterals
Parallelogram: Element & its Property
Some Special Parallelograms
Application based questions
Chapter 4 Data Handling
0/5
Introduction to Data
Types of Data Representation
Drawing PI Chart
Chance and Probability
Chance and Probability in Real Life
Chapter 5 Squares and Square Number
0/7
Concept of Square Numbers and Perfect Squares
Properties of Square Numbers
Interesting Patterns in Square Numbers
Finding the Square of a Number
Pythagorean triplets
Concept of Square Root
Different Methods to Find Square Roots
Chapter 6 Cubes and Cube Roots
0/3
Introduction of cubes and its properties
Intresting Pattern in Cubes
cube roots and its finding way
Chapter 7 Comparing quantities
0/5
Introduction of Ratio & Percentage
Concept of Discount
Sales Tax/Value Added Tax/Goods and Ser vices Tax
Compound Interest: Concept, Formula, and Applications
formulas summary
Chapter 8 Algebraic Expressions and Identities
0/2
introduction
Addition, substraction & Multiplication of algebric expressions
Chapter 9 Mensuration
0/7
What we are going to learn in this chapter
Area of Polygon
Introduction of Solid Shape
Surface Area of Cubical, Cuboid and Cylinder
Volume of Cube, Cuboid and Cylinder
Understanding Capacity and its Relation to Volume
Complete List of Formulas
Chapter 10 Exponents and Powers
0/3
Introduction to Exponents
Rules for Exponent Rules
Express Large and Small Numbers in Standard Form
Chapter 11 Direct and Inverse Proportions
0/3
Direct Proportion
Inverse Proportions
Real-Life Examples & Uses
Chapter 12 Factorization
0/7
Introduction to Factorization
Methods of Factorization
Common Factor Method of Factorization
Regrouping Method of Factorization
Factorization Using Identities
Factorization by Splitting the Middle Term
Division of Algebraic Expressions
Introduction to Graphs
0/2
Introduction to Graphs
Applications of Graphs
CBSE Class 8 Maths
About Lesson

Area of a Polygon

To determine the area of a polygon, we divide it into simpler shapes such as triangles and trapeziums and calculate their individual areas. Below two figures has been given:

Method 1: Using Two Diagonals (Fig 9.1)

  • By drawing two diagonals AC and AD, the pentagon ABCDE is divided into three triangles:
  • Area of ABCDE=Area of △ABC+Area of △ACD+Area of △AED
  • This method simplifies the calculation by breaking the pentagon into three non-overlapping triangles.

Method 2: Using One Diagonal and Two Perpendiculars (Fig 9.2)

  • By drawing one diagonal AD and two perpendiculars BF and CG, the pentagon ABCDE is divided into four parts:
  • Area of ABCDE=Area of △AFB+Area of trapezium BFGC+Area of △CGD+Area of △AED
  • This method is useful when working with trapeziums and right-angled triangles, making area calculations more manageable.
  • Parallel sides of trapezium BFGC should be identified for its area calculation.

These methods help in computing the area of irregular polygons effectively by breaking them into known geometric shapes.

 For solving the questions directly , Here are the formulas for the area of a parallelogram, trapezium, rhombus, and triangle, along with their explanations:

1. Area of a Parallelogram

A parallelogram is a quadrilateral with opposite sides equal and parallel.

Formula:

Area=Base×Height,

where

  • Base (b) = Any one of the sides of the parallelogram
  • Height (h) = The perpendicular distance between the opposite sides.

  • 2. Area of a Trapezium

    A trapezium (or trapezoid) is a quadrilateral with one pair of opposite sides parallel.

    Formula:

    Area=12×(Base1+Base2)×Height

    Where:

    • Base₁ and Base₂ = The lengths of the two parallel sides
    • Height (h) = The perpendicular distance between the parallel sides

  • 3. Area of a Rhombus

    A rhombus is a quadrilateral with all sides equal in length and opposite angles equal.

    Formula:

    Area=12×Diagonal1×Diagona

    Where:

    • Diagonal₁ and Diagonal₂ = The lengths of the two diagonals

    4. Area of a Triangle

    A triangle is a three-sided polygon.

    Formula:

    Area=12×Base×Height

    Where:

    • Base (b) = Any side of the triangle
    • Height (h) = The perpendicular distance from the base to the opposite vertex
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