Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Mensuration → Area and Perimeter ↓


Area of Quadrilaterals


In this lesson, we're going to dive into the fascinating world of quadrilaterals, focusing mainly on understanding how to calculate their areas. A quadrilateral is a polygon with four sides, which also means it has four angles. Some common examples of quadrilaterals are squares, rectangles, parallelograms, trapezoids, and rhombuses. Finding the area of these shapes may seem daunting at first, but once it's broken down, the process becomes quite simple and logical.

Basic concepts

Let us first understand some basic geometry concepts and terminologies that are needed to perform area calculations effectively:

  • Vertices: The points where two sides of a shape meet. In a quadrilateral, there are four vertices.
  • Sides: Line segments between vertices. A quadrilateral has four sides.
  • Diagonal: A line segment joining two disjoint vertices.
  • Base and height: Used to calculate the area of some quadrilaterals. The base is one side of the quadrilateral, and the height is the perpendicular distance from the base to the opposite side.

Calculating the area of specific quadrilaterals

1. Area of a square

A square is a quadrilateral with all four sides of equal length and all angles equal to 90 degrees. The formula for finding the area of a square is simple:

        Area = side × side = side 2

Example: If the length of the side of a square is 5 cm, then its area will be:

        Area = 5 cm × 5 cm = 25 cm 2
    
    
      
      5 cm

2. Area of a rectangle

A rectangle is a quadrilateral whose opposite sides are equal and all angles are equal to 90 degrees. The formula for the area of a rectangle is:

        Area = length × breadth

Example: If the length is 8 cm and the width is 3 cm, then the area will be:

        Area = 8 cm × 3 cm = 24 cm 2
    
    
      
      8 cm
      3 cm

3. Area of parallelogram

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal in length. Its area can be found using the base and height:

        Area = base × height

Example: If the base is 6 cm and the height is 4 cm, what is the area?

        Area = 6 cm × 4 cm = 24 cm 2
    
    
      
      6 cm
      4 cm

4. Area of trapezium

A trapezoid (or trapezium in some countries) is a quadrilateral with one pair of parallel sides. The area formula for a trapezoid is a little more complicated:

        Area = (1/2) × (base1 + base2) × height

Example: If base 1 is 10 cm, base 2 is 6 cm, and the height is 4 cm, then its area will be:

        Area = (1/2) × (10 cm + 6 cm) × 4 cm 
             = (1/2) × 16 cm × 4 cm 
             = 32 cm 2
    
    
      
      10 cm
      6 cm
      4 cm

5. Area of rhombus

A rhombus is a quadrilateral with all four sides of equal length. Its area can be found using the lengths of its diagonals:

        Area = (1/2) × d1 × d2

Example: If the diagonal d1 is 8 cm and the diagonal d2 is 6 cm, then the area is:

        Area = (1/2) × 8 cm × 6 cm 
             = 24 cm 2
    
    
      
      
      
      8 cm
      6 cm

Additional lesson examples and exercises

Let's take a look at some practice examples and additional scenarios so that you can better understand the concept of calculating the area of quadrilaterals.

Example 1: Imagine you are creating a rectangular shaped garden that is 12 meters long and 5 meters wide. How much area will your garden cover?

        Area = length × breadth 
             = 12 m × 5 m 
             = 60 m 2

Example 2: You have a square picture frame with a side of 15 cm. Find the area of the picture frame.

        Area = side × side 
             = 15 cm × 15 cm 
             = 225 cm2

Example 3: A trapezoid shaped plot has bases 20 m and 14 m and its height is 10 m. Find the total area of the land.

        Area = (1/2) × (base1 + base2) × height 
             = (1/2) × (20 m + 14 m) × 10 m 
             = 170 m 2

Visual understanding of quadrilaterals

Visual representations can significantly aid in the understanding and retention of mathematical concepts. Here is another illustration of the types of quadrilaterals, showing their essential features.

    
      
      
      Social class

      
      
      rectangle

      
      
      Quadrilateral

      
      
      Quadrilateral

Conclusion

Understanding the area of quadrilaterals is an essential part of geometry. In everyday life, you may need to apply this knowledge when planning construction projects, purchasing materials, or designing space layouts. Mastering these formulas is the key to solving real-world problems effectively and efficiently.

Overall, memorize the specific formulas for each quadrilateral shape, practice visualizing the problem, and apply the formulas where needed. With these skills, you'll be well on your way to conquering problems involving the area of quadrilaterals. Happy calculating!


Grade 8 → 4.1.3


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Area of Triangles
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Area of Quadrilaterals

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