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 → Geometry → Quadrilaterals ↓


Types of Quadrilaterals


Quadrilaterals are a group of polygons that have four sides, four corners or vertices, and four angles. They are a common shape in geometry and understanding them is an important part of learning about shapes. There are different types of quadrilaterals, each with their own distinct properties.

Let's look at these types, understand their properties and see how they differ from each other. We will also see how to identify and use these quadrilaterals through examples and figures.

Understanding quadrilaterals

First, let's define some general properties of quadrilaterals:

  • They all have four sides and four vertices.
  • The sum of all the interior angles of a quadrilateral is always 360 degrees. You can demonstrate this using the formula: 
    (n - 2) × 180°
    where n is the number of sides. For quadrilaterals, n = 4, so (4 - 2) × 180° = 360°.

Types of quadrilaterals

1. Square

A square is a special type of quadrilateral that is highly symmetrical. It has some unique properties:

  • All sides are equal in length.
  • All interior angles are 90 degrees.
  • Its diagonals are equal and bisect each other at right angles.
A square with all sides equal and angles of 90 degrees.

For example, if you draw a square and measure its sides, you will find that they are equal, and each angle is 90 degrees. If you draw lines from one corner to the other, those lines are diagonals, and they will meet exactly in the middle.

2. Rectangle

A rectangle is like an extended square, only the opposite sides are equal, and its properties are:

  • The opposite sides are equal in length.
  • All interior angles are 90 degrees.
  • The diagonals are equal but do not bisect at right angles.
A rectangle with opposite sides equal and angles of 90 degrees.

In a rectangle, every angle is a right angle. Rectangles are very common in everyday life, as many books, papers, and screens are rectangular in shape.

3. Rhombus

A rhombus is a quadrilateral in which all sides are equal, but unlike a square, the angles can be of different measures. Its properties are as follows:

  • All sides are of equal length.
  • Opposite angles are equal.
  • The diagonals bisect each other at right angles.
A rhombus whose all sides are equal but the angles are not 90 degrees.

An example of a rhombus is the diamond shape, often seen in playing cards. If you look at the diagonals, they intersect each other at right angles, but are not equal in length.

4. Parallelogram

A parallelogram is a quadrilateral whose opposite sides are parallel. Its properties are:

  • The opposite sides are equal in length.
  • Opposite angles are equal.
  • Adjacent angles are supplementary, that is, their sum is 180 degrees.
  • The diagonals bisect each other.
A parallelogram whose opposite sides are parallel and equal in length.

One way to identify a parallelogram is to check whether both pairs of opposite sides are parallel. An everyday example of a parallelogram is the shape of a window curtain.

5. Trapezium

The trapezoid, also called a trapezium in some countries, is a quadrilateral that has only one pair of parallel sides. Its properties include:

  • One pair of opposite sides are parallel.
  • The non-parallel sides are called legs.
  • Angles on the same side of the leg are complementary.
A trapezoid with one pair of parallel sides.

An example of a trapezoid is a bridge like you might see in children's playgrounds. Another example is the lid of a toothpaste tube.

6. Kite

Kites have a distinctive shape and the following characteristics:

  • Two pairs of adjacent sides are equal.
  • A pair of opposite angles are equal, which is between unequal sides.
  • Diagonals bisect each other at right angles.
A kite with two pairs of adjacent sides equal.

If you see a kite flying in the sky on a windy day, you will easily recognize its shape. The top and bottom pair are of the same length, which gives kites their unique shape.

Exploring properties with examples

Let us take a closer look at examples demonstrating simple mathematical calculations involving these quadrilaterals.

Calculating perimeter:

The perimeter of a quadrilateral is simply the distance around the shape, calculated by adding up the lengths of its sides.

Perimeter of a Quadrilateral = AB + BC + CD + DA

For a square, since all sides are equal:

Perimeter of a Square = 4 × side

If the length of the side of a square is 10 units, then its perimeter is:

Perimeter = 4 × 10 = 40 units

Calculation of area:

Each type of quadrilateral has a different formula to find its area. Here are some formulas:

For rectangles and squares:

Area = length × width

In a rectangle of length 8 units and breadth 5 units:

Area = 8 × 5 = 40 square units

For a parallelogram:

Area = base × height

For trapezium:

Area = 1/2 × (base1 + base2) × height

If the base of a trapezium is 7 units and 5 units and the height is 4 units, then what will be the area?

Area = 1/2 × (7 + 5) × 4 = 1/2 × 12 × 4 = 24 square units

Importance of quadrilateral

Understanding quadrilaterals is essential not only for academic purposes but also for real-world applications. They are found everywhere, from the design of everyday objects to the construction of buildings. By learning to recognize and calculate their properties, we open ourselves up to a deeper understanding of the world around us. Quadrilaterals serve as a basic building block for geometry that extends into advanced studies and various professions.

We hope this exploration has given you clarity about the diverse world of quadrilaterals. Continue practicing to identify and draw these shapes, calculate their perimeter and area, and use them in real life.


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