Grade 10
  1. Number Systems  1.1. Real Numbers  1.1.1. Properties of Real Numbers  1.1.2. Rational and Irrational Numbers  1.1.3. Decimal Representation of Real Numbers  1.1.4. Operations on Real Numbers  1.1.5. Real Numbers on the Number Line  1.2. Euclid's Division Lemma  1.3. Prime Factorization  1.4. LCM and HCF  1.5. Exponents and Radicals  1.5.1. Laws of Exponents  1.5.2. Simplifying Radical Expressions  1.5.3. Scientific Notation
  2. Algebra  2.1. Polynomials  2.1.1. Definition and Types of Polynomials  2.1.2. Degree of a Polynomial  2.1.3. Zeros of a Polynomial  2.1.4. Factorization of Polynomials  2.1.5. Algebraic Identities  2.2. Linear Equations in Two Variables  2.2.1. Graph of Linear Equations  2.2.2. Solutions of Linear Equations  2.2.3. Application of Linear Equations in Word Problems  2.3. Quadratic Equations  2.3.1. Standard Form of a Quadratic Equation  2.3.2. Methods of Solving Quadratic Equations  2.3.2.1. Factorization Method  2.3.2.2. Completing the Square Method  2.3.2.3. Quadratic Formula  2.3.3. Nature of Roots  2.4. Arithmetic Progressions  2.4.1. Definition of Arithmetic Progression  2.4.2. General Term of an AP  2.4.3. Sum of First n Terms of an AP  2.5. Introduction to Functions  2.5.1. Definition and Types of Functions  2.5.2. Domain and Range  2.5.3. Composition of Functions  2.5.4. Inverse of a Function
  3. Coordinate Geometry  3.1. Cartesian System  3.2. Distance Formula  3.3. Section Formula  3.4. Area of a Triangle  3.5. Slope of a Line  3.6. Equation of a Line  3.6.1. Slope-Intercept Form  3.6.2. Point-Slope Form  3.6.3. Two-Point Form  3.6.4. Intercept Form  3.6.5. General Form of a Line
  4. Trigonometry  4.1. Trigonometric Ratios  4.1.1. Sine Cosine Tangent and their Reciprocals  4.1.2. Values of Trigonometric Ratios at Specific Angles  4.2. Trigonometric Identities  4.3. Trigonometric Ratios of Complementary Angles  4.4. Heights and Distances  4.4.1. Angle of Elevation and Depression  4.4.2. Applications in Real-Life Problems
  5. Geometry  5.1. Triangles  5.1.1. Congruence of Triangles  5.1.2. Criteria for Congruence  5.1.3. Properties of Triangles  5.2. Similarity  5.2.1. Similar Figures  5.2.2. Criteria for Similarity  5.2.3. Similarity of Triangles  5.2.4. Applications of Similarity in Real-Life  5.3. Circles  5.3.1. Properties of a Circle  5.3.2. Tangent to a Circle  5.3.3. Number of Tangents from a Point  5.3.4. Angle Subtended by an Arc  5.4. Constructions  5.4.1. Construction of Similar Triangles  5.4.2. Tangent to a Circle  5.4.3. Construction of Angle Bisectors
  6. Mensuration  6.1. Areas of Plane Figures  6.1.1. Area of a Triangle  6.1.2. Area of a Parallelogram  6.1.3. Area of a Trapezium  6.1.4. Area of a Rhombus  6.2. Surface Areas and Volumes  6.2.1. Surface Area of a Cube Cuboid and Cylinder  6.2.2. Surface Area of a Cone and Sphere  6.2.3. Volume of a Cube Cuboid and Cylinder  6.2.4. Volume of a Cone and Sphere  6.3. Conversion of Units  6.4. Frustum of a Cone
  7. Statistics  7.1. Introduction to Statistics  7.2. Collection of Data  7.3. Presentation of Data  7.3.1. Tabular Form  7.3.2. Graphical Form  7.3.2.1. Bar Graph  7.3.2.2. Histogram  7.3.2.3. Frequency Polygon  7.3.2.4. Ogive  7.4. Measures of Central Tendency  7.4.1. Mean Median and Mode  7.4.2. Quartiles and Percentiles  7.5. Measures of Dispersion  7.5.1. Range and Interquartile Range  7.5.2. Standard Deviation and Variance
  8. Probability  8.1. Introduction to Probability  8.2. Experimental Probability  8.3. Theoretical Probability  8.4. Probability of Simple Events  8.5. Complementary Events  8.6. Probability of Compound Events

Grade 10 → Mensuration → Areas of Plane Figures ↓


Area of a Trapezium


In the field of geometry, a trapezoid is a unique quadrilateral that has special properties. Generally, a trapezoid is defined as a four-sided figure or quadrilateral that has a pair of parallel sides. These parallel sides are important because they form the basis for calculating the area of a trapezoid. Understanding how to find the area of a trapezoid is a fundamental part of studying geometry and measurement, especially in grade 10 maths.

Defining trapezium

Let's start by clearly defining what a trapezoid is. Imagine any four-sided figure. If this figure has one pair of sides parallel, then it is a trapezoid. These sides are often called "bases" Unlike parallelograms, trapezoids do not have both pairs of opposite sides parallel, which adds a special twist to calculating their areas.

Base 1 (B1) Base 2 (B2) Height(H)

Main parts of trapezium

  • Base 1 (b1): One of the parallel sides.
  • Base 2 (b2): The other parallel side.
  • Height (h): The perpendicular distance between base 1 and base 2.

It is important to understand the concept of "height" in a trapezoid, because it is different from the sides of the shape. The height is always the perpendicular distance, meaning it forms right angles with the bases. This is important because it affects That's how we calculate area.

Area formula

The formula for finding the area of a trapezoid is given by the following equation:

Area = 0.5 × (Base1 + Base2) × Height

In terms of symbols, we often represent this formula as:

A = 0.5 × (b1 + b2) × h

Here:

  • A stands for area.
  • b1 represents base1.
  • b2 represents base 2.
  • h represents the height.

Formula derivation

To understand why this formula is used, let's imagine a trapezoid and break it down. A trapezoid can be thought of as a number of triangles joined together. Trapezoids can be thought of as simple geometric shapes, such as triangles or rectangles. By dividing into, we get a simple way to calculate the area by adding the areas of these interior parts. However, the given formula makes this process very concise and efficient.

Example calculation

Let us look at some examples to strengthen our understanding of the area of a trapezoid.

Example 1

Imagine a trapezoid where base 1 is 8 cm, base 2 is 5 cm, and the height is 4 cm. Putting these into our formula, we get:

A = 0.5 × (8 + 5) × 4 = 0.5 × 13 × 4 = 26 cm²

Thus, the area of this trapezoid is 26 square centimeters.

Example 2

Consider a trapezoid with base 1 10 m, base 2 7 m, and height 6 m. Using the formula:

A = 0.5 × (10 + 7) × 6 = 0.5 × 17 × 6 = 51 m²

Here, the area of the trapezium is 51 square meters.

Understanding through practical examples

Imagine you have a trapezoid-shaped garden, and you want to plant some new grass. To order the right quantity, you need to calculate the area.

Suppose one parallel side of your garden (base 1) is 15 meters, the other parallel side (base 2) is 10 meters, and the distance (height) between these two sides is 8 meters.

A = 0.5 × (15 + 10) × 8 = 0.5 × 25 × 8 = 100 m²

So, you will need enough grass to cover 100 square meters of area.

Care for practical variations

In real-world situations, shapes may not always conform to the ideal measurements, yet the formula still applies as long as you can identify the base and height.

Visualizing more trapezoid shapes

Below are some pictures of trapeziums with different side lengths, which will help in understanding this concept.

B1 B2 H Base 1 (B1) Base 2 (B2) Height(H)

Conclusion on area of trapezium

Despite their two-dimensional simplicity, trapezoids hold an important place in geometric studies. Understanding how to calculate their area using base and height is important, especially when used in practical applications such as construction, land measurement, and design. The problems are resolved.

Mastering the formula:

A = 0.5 × (b1 + b2) × h

Prepares students and practitioners alike to tackle a variety of real-world challenges involving trapezoid shapes. The simplicity and effectiveness of this formula allows it to be employed with confidence and accuracy in both theoretical and practical scenarios.


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Area of a Parallelogram
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Area of a Rhombus

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Area of a Trapezium

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