Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Mensuration → Area ↓


Area of Trapezium


Geometry is a branch of mathematics that deals with the properties of shape, measurement, and space. In this lesson, we will find the area of a specific quadrilateral called a trapezoid. A trapezoid is a four-sided plane shape with parallel sides. has a pair of sides. Let's dive into the world of trapezoids and understand how to find their area.

What is a trapezoid?

A trapezoid is a quadrilateral in which one pair of sides is parallel. The parallel sides of a trapezoid are usually called "bases", and the non-parallel sides are called "legs". The height of a trapezoid is the perpendicular between the bases The bases can have different lengths, and the shape itself can look like an oblique rectangle or a more irregular quadrilateral.

Base 1 Base 2 Height

Formula for the area of a trapezoid

The formula for finding the area of a trapezoid depends on its base and height. The area of a trapezoid can be found using the following formula:

Area = ½ × (Base_1 + Base_2) × Height
Area = ½ × (Base_1 + Base_2) × Height

Let's break down this formula:

  • base_1 is the length of one of the parallel sides.
  • Base_2 is the length of the second parallel side.
  • The height is the perpendicular distance between the two bases.

This formula basically works by finding the average length of the two bases, multiplying it by the height, and then dividing by two to get the shape of the trapezoid.

Step-by-step calculation

Let's calculate the area of a trapezoid using specific measurements as an example.

Consider a trapezoid where base_1 is 8 cm, base_2 is 5 cm, and height is 4 cm.

Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (8 + 5) × 4 Area = ½ × 13 × 4 Area = 26
Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (8 + 5) × 4 Area = ½ × 13 × 4 Area = 26

Thus, the area of the trapezium is 26 square centimeters.

More examples with visuals

Let's consider another example to deepen our understanding:

Imagine a trapezoid with base_1 of 14 m, base_2 of 10 m and height of 6 m. We can look at it like this:

14 meters 10 minutes 6 
Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (14 + 10) × 6 Area = ½ × 24 × 6 Area = 72
Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (14 + 10) × 6 Area = ½ × 24 × 6 Area = 72

The area of this trapezium is 72 square meters.

Practical applications

Understanding the area of a trapezoid is useful in real life. For example, if you need to find the surface area of an area on the ground with parallel boundaries (such as a backyard or a decorating mat), finding the area of a trapezoid can be beneficial. Similarly, this concept is applied in interior designing, land measurement and architectural drafting.

Practice problems

Let's try to solve some problems to practice the concept of finding the area of a trapezoid.

  1. The bases of a trapezium are 12 m and 18 m. If the height is 5 m, what is the area?
  2. Find the area of a trapezium whose bases are 15 cm and 7 cm and height is 4 cm.
  3. You need to cover a trapezoid-shaped garden with grass. The parallel sides measure 20 feet and 12 feet respectively. The height of the garden is 8 feet. How many square feet of grass will you need?

Solving practice problems

Let us solve each problem step-by-step.

  1. Problem 1:
    Given: base_1 = 12 m, base_2 = 18 m, height = 5 m 
            Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (12 + 18) × 5 Area = ½ × 30 × 5 Area = 75
        Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (12 + 18) × 5 Area = ½ × 30 × 5 Area = 75
    Its area is 75 square meters.
  2. Problem 2:
    Given: base_1 = 15 cm, base_2 = 7 cm, height = 4 cm 
            Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (15 + 7) × 4 Area = ½ × 22 × 4 Area = 44
        Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (15 + 7) × 4 Area = ½ × 22 × 4 Area = 44
    Its area is 44 square centimeters.
  3. Problem 3:
    Given: base_1 = 20 ft, base_2 = 12 ft, height = 8 ft 
            Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (20 + 12) × 8 Area = ½ × 32 × 8 Area = 128
        Area = ½ × (Base_1 + Base_2) × Height Area = ½ × (20 + 12) × 8 Area = ½ × 32 × 8 Area = 128
    You will need 128 square feet of grass.

Common mistakes to avoid

  • Confusing the height with the length of non-parallel sides. Always remember that the height is perpendicular to the bases.
  • Forgetting to divide by 2 in the formula. The formula already takes into account that we are dealing with a trapezoid, not a rectangle.
  • Mixing units of measurement. Make sure your units are consistent when calculating area.

Conclusion

Finding the area of a trapezoid is a fundamental math skill that combines basic arithmetic and geometry. It's important to understand the role of each part of the trapezoid — such as the base and height — and how these measurements come together in the area formula. Practice is key to mastering the concept, allowing you to effectively apply it in a variety of real-world contexts. Keep exploring and practicing geometry, as it is a vital way of understanding the space and forms around us. Provides a structured approach.


Grade 6 → 5.2.4


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Area of Trapezium

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