Definition Properties Formulas and Solved Examples of Quadrilaterals
The concept of types of quadrilaterals plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding these shapes builds a strong foundation for geometry and logical reasoning in students.
What Is Types of Quadrilaterals?
A quadrilateral is a two-dimensional (2D) polygon with four sides, four vertices, and four angles. Types of quadrilaterals include shapes like rectangles, squares, parallelograms, rhombuses, kites, and trapeziums. You’ll find this concept applied in areas such as geometry calculations, logical MCQs, and real-life measurements of objects like fields and rooms.
Classification of Quadrilaterals
Quadrilaterals can be classified based on their side lengths, angles, and parallel sides. Here’s a quick comparison chart for the types of quadrilaterals and their properties:
| Type | Sides | Angles | Diagonals | Key Properties |
|---|---|---|---|---|
| Square | All sides equal | All 90° | Equal, perpendicular & bisect | All sides & angles equal, 2 lines of symmetry |
| Rectangle | Opposite sides equal | All 90° | Equal & bisect | Opposite sides equal, 2 lines of symmetry |
| Rhombus | All sides equal | Opposite angles equal | Perpendicular & bisect | All sides equal, diagonals not equal |
| Parallelogram | Opposite sides equal | Opposite angles equal | Bisect each other | Opposite sides & angles equal |
| Trapezium (Trapezoid) | Two sides parallel | Angles vary | No special property | Only one pair of parallel sides |
| Kite | 2 pairs of equal adjacent sides | 1 pair opposite angles equal | Perpendicular, one bisects the other | One axis of symmetry, diagonals perpendicular |
Properties of Each Quadrilateral
Let’s look at the main types of quadrilaterals and their key properties with common real-life examples:
1. Square
- All four sides and all four angles are equal (each 90°).
- Each diagonal splits the square into two equal triangles.
- Example: Chessboard square, windowpane.
2. Rectangle
- Opposite sides are equal and parallel.
- All angles are right angles (90°).
- Example: Book page, cupboard door.
3. Parallelogram
- Both pairs of opposite sides are equal and parallel.
- Opposite angles are equal, but angles don’t need to be 90°.
- Example: Slanted desk surface.
4. Rhombus
- All sides equal in length.
- Diagonals intersect at right angles and bisect each other.
- Example: Diamond, kite (sometimes called a diamond shape).
5. Trapezium (Trapezoid)
- Only one pair of sides is parallel (called bases).
- Non-parallel sides are called legs.
- Example: Table with slanting legs, handbag design.
6. Kite
- Two pairs of adjacent sides are equal.
- Diagonals cross at right angles.
- Example: Flying kite, some lanterns.
Special Properties & Relationships
Some types of quadrilaterals are special cases of others. For example:
- Every square is a rectangle and a rhombus, but not every rectangle/rhombus is a square.
- All rectangles, rhombuses, and squares are parallelograms.
This relationship can be visualized using a Venn diagram, which helps clarify MCQs and concept-based questions. For more details, read Classify Quadrilaterals and Difference Between Square and Rectangle.
Key Formulas for Types of Quadrilaterals
| Quadrilateral | Area Formula | Perimeter Formula |
|---|---|---|
| Square | Area = (side)2 | Perimeter = 4 × side |
| Rectangle | Area = length × width | Perimeter = 2 × (length + width) |
| Parallelogram | Area = base × height | Perimeter = 2 × (side1 + side2) |
| Rhombus | Area = (d1 × d2) / 2 | Perimeter = 4 × side |
| Trapezium | Area = ½ × (sum of parallel sides) × height | Perimeter = sum of all sides |
| Kite | Area = ½ × (product of diagonals) | Perimeter = 2 × (sum of adjacent sides) |
Step-by-Step Illustration: Example Problem
Question: If one angle of a parallelogram is 70°, what are the remaining angles?
1. In a parallelogram, opposite angles are equal, and adjacent angles are supplementary.2. If one angle is 70°, the opposite angle is also 70°.
3. Adjacent angles = 180° – 70° = 110° (because adjacent angles add up to 180°).
4. So, the four angles are: 70°, 110°, 70°, 110°.
Try These Yourself
- List all quadrilaterals that have both pairs of opposite sides parallel.
- Is every rectangle a square?
- Find the perimeter of a kite with sides 8 cm and 6 cm (adjacent pairs).
- Identify the special quadrilaterals among: Windowpane, Desk, Chessboard, Kite.
Relation to Other Concepts
The concept of types of quadrilaterals connects closely to types of polygons, area of quadrilaterals, and rectangle properties. By mastering this, you can tackle perimeter, area, diagonal length, and symmetry problems much more easily.
Classroom Tip
A handy way to remember types of quadrilaterals: “All squares are rectangles and rhombuses, but the reverse is not always true!” Vedantu’s teachers often use such tips and symmetry charts during live sessions to make the differences stick in your mind.
We explored types of quadrilaterals—from definition, chart, properties, real-life examples, formulas, and difference questions. With regular practice and live classes on Vedantu, you can quickly identify, classify, and solve any quadrilateral geometry problem for school and competitive exams.
Related reads: Properties of Parallelogram, Rectangle, Rhombus, Area of Quadrilateral, Types of Polygons
FAQs on Types of Quadrilaterals in Geometry
1. What are the types of quadrilaterals?
The main types of quadrilaterals are square, rectangle, parallelogram, rhombus, trapezium (trapezoid), and kite. A quadrilateral is any polygon with four sides and four angles.
- Square: All sides equal and all angles 90°.
- Rectangle: Opposite sides equal and all angles 90°.
- Parallelogram: Opposite sides parallel and equal.
- Rhombus: All sides equal, opposite angles equal.
- Trapezium (Trapezoid): At least one pair of parallel sides.
- Kite: Two pairs of adjacent equal sides.
2. What is a quadrilateral in geometry?
A quadrilateral is a closed polygon with four sides, four vertices, and four angles. The sum of its interior angles is always 360°. Quadrilaterals can be regular or irregular depending on their side lengths and angles.
3. What is the sum of interior angles of a quadrilateral?
The sum of the interior angles of any quadrilateral is 360°. This can be found using the polygon formula:
- Sum of angles = (n − 2) × 180°
- For a quadrilateral, n = 4
- (4 − 2) × 180° = 360°
4. What is the difference between a square and a rectangle?
The main difference is that a square has all sides equal, while a rectangle has only opposite sides equal. Both shapes have:
- All interior angles equal to 90°
- Opposite sides parallel
5. What are the properties of a parallelogram?
A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel. Its key properties are:
- Opposite sides are equal and parallel
- Opposite angles are equal
- Consecutive angles are supplementary (sum to 180°)
- Diagonals bisect each other
6. What is a trapezium (trapezoid)?
A trapezium (trapezoid) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. If the non-parallel sides are equal, it is called an isosceles trapezium.
7. What is the formula for the area of different quadrilaterals?
The area formulas depend on the type of quadrilateral:
- Square: Area = side²
- Rectangle: Area = length × breadth
- Parallelogram: Area = base × height
- Rhombus: Area = (1/2) × d₁ × d₂
- Trapezium: Area = (1/2) × (sum of parallel sides) × height
8. What is a rhombus and how is it different from a square?
A rhombus is a quadrilateral with all sides equal, but its angles are not necessarily 90°. Differences from a square:
- Rhombus angles are not always right angles.
- Square has all angles equal to 90°.
- Both have equal sides and diagonals that bisect each other.
9. What is a kite in geometry?
A kite is a quadrilateral with two pairs of adjacent equal sides. Its important properties include:
- One pair of opposite angles are equal
- Diagonals intersect at 90°
- One diagonal bisects the other
10. How do you identify different types of quadrilaterals?
You can identify types of quadrilaterals by checking their sides, angles, and diagonals. Follow these steps:
- Check if opposite sides are parallel → Parallelogram or trapezium.
- Check if all angles are 90° → Rectangle or square.
- Check if all sides are equal → Rhombus or square.
- Check for two pairs of adjacent equal sides → Kite.
