How to Identify Different Types of Quadrilaterals with Examples
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 and Their Properties
1. What are the main types of quadrilaterals?
The main types of quadrilaterals are parallelograms (including rectangles and squares), rhombuses, trapeziums (or trapezoids), and kites. A general quadrilateral is also a category encompassing shapes that don't fit into the other specific types.
2. How do you identify a parallelogram versus a rhombus?
Both are quadrilaterals with opposite sides parallel. However, a rhombus has all four sides equal in length, while a parallelogram only requires opposite sides to be equal. A square is a special case of both a parallelogram and a rhombus.
3. What are the properties of a kite in maths?
A kite has two pairs of adjacent sides that are equal in length. Its diagonals are perpendicular to each other, and only one diagonal is bisected by the other.
4. Is every square a rectangle?
Yes, every square is a rectangle. A rectangle is a quadrilateral with four right angles; a square meets this requirement, plus the added condition of having all four sides equal in length.
5. How many degrees are the angles in a quadrilateral?
The sum of the interior angles of any quadrilateral is always 360 degrees.
6. Which quadrilaterals have both pairs of opposite sides parallel?
Parallelograms (including rectangles, rhombuses, and squares) have both pairs of opposite sides parallel. Trapeziums only have one pair of parallel sides.
7. What is the difference between a trapezium and a parallelogram?
A trapezium (or trapezoid) has only one pair of parallel sides, while a parallelogram has two pairs of parallel sides.
8. What are the properties of a rectangle?
A rectangle has four right angles (90°), opposite sides are parallel and equal in length, and its diagonals bisect each other.
9. How are the diagonals of a rhombus related?
The diagonals of a rhombus are perpendicular bisectors of each other. This means they intersect at a right angle, and each diagonal cuts the other in half.
10. What is a concave quadrilateral?
A concave quadrilateral has at least one interior angle greater than 180 degrees. This means that at least one of its vertices points inwards, creating a 'dent' in the shape.
11. What is the area formula for a parallelogram?
The area of a parallelogram is calculated by multiplying its base by its height: Area = base × height.
12. Can a kite be a rhombus?
Yes, a kite can be a rhombus. If a kite has all four sides equal, it becomes a rhombus (and in fact, a square if it also has right angles).
