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 → Geometry → Understanding Quadrilaterals → Types of Quadrilaterals ↓


Trapezium


In the world of geometry, shapes and figures are important components. They not only enhance our understanding of the world around us but also help in developing precise mathematical concepts. The most frequently encountered problem in the study of quadrilaterals is the shape and size of the figure. One such geometric shape is the trapezium.

What is a trapezoid?

A trapezoid is a type of quadrilateral. A quadrilateral is a four-sided polygon with four angles. A trapezoid, specifically, is a quadrilateral with at least one pair of parallel sides. These parallel sides are called the bases of the trapezoid, and the nonparallel sides are called legs.

Properties of trapezium

  • It has four arms.
  • It has a pair of parallel sides.
  • It has four angles and the sum of all interior angles is always 360 degrees.

Visual representation of trapezium

A B C D

In the example above, the quadrilateral ABCD is a trapezoid, where the side AB is parallel to the side CD. Points A, B, C, and D are the vertices of the trapezoid.

Types of trapezoids

1. Isosceles trapezoid

Isosceles trapezium is a trapezium which has the following properties:

  • The non-parallel sides (legs) are equal in length.
  • Opposite angles are equal.
A B C D

In the above isosceles trapezium ABCD, AB is parallel to CD, and AD is equal to BC.

2. Right trapezium

A right trapezoid has a pair of parallel sides and one or two right angles. This means that at least one angle in a right trapezoid is 90 degrees.

A B C D

Here, in the right-angled trapezium ABCD, the sides AB and CD are parallel, and the angles DAB and ABC are right angles.

Area of trapezium

The area of a trapezoid can be calculated using the following formula:

Area = 0.5 * (Base1 + Base2) * Height

Where:

  • Base1 and Base2 are the lengths of two parallel sides.
  • Height is the perpendicular distance between the parallel sides.

Let's find the area of a trapezoid with bases of 8 cm and 5 cm and a height of 4 cm.

Area = 0.5 * (8 + 5) * 4 = 0.5 * 13 * 4 = 26 cm²

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

Perimeter of trapezium

The perimeter of a trapezoid is obtained by summing the lengths of all its sides. If the sides are called a, b, c, and d, then the perimeter is:

Perimeter = a + b + c + d

For example, if the sides of a trapezoid are 6 cm, 9 cm, 5 cm, and 7 cm, then the perimeter is:

Perimeter = 6 + 9 + 5 + 7 = 27 cm

Thus, the perimeter of the trapezoid is 27 cm.

Examples of trapezia in real life

Trapezias are not just confined to textbooks; they appear in a variety of forms in our daily lives. Some real-world examples include:

  • Desks, which are made in a trapezoid shape for ergonomic purposes.
  • The design of some bridges and architectural structures often incorporates the trapezoid shape for stability.
  • Trapezoid-shaped tables or cabinets that fit into specific spaces.

Conclusion

Trapezoid is a fascinating figure that exemplifies the beauty and functionality of geometric shapes. Its properties and types provide important insights into quadrilateral classification. Understanding trapezoids also helps in the application of geometric principles to solve complex problems. As students advance in geometry, mastering the concept of a trapezoid lays a solid foundation for more sophisticated mathematical explorations.


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