Types of Quadrilaterals
A quadrilateral is a closed shape with four sides. But not all quadrilaterals look the same. Some have equal sides, some have parallel sides, some have right angles.
Based on the properties of their sides and angles, quadrilaterals are classified into different types — rectangle, square, parallelogram, rhombus, trapezium, and kite.
In Class 6, you will learn to identify each type by looking at its special properties.
What is Types of Quadrilaterals - Grade 6 Maths (Understanding Elementary Shapes)?
Types of quadrilaterals:
- Parallelogram: Both pairs of opposite sides are parallel and equal.
- Rectangle: A parallelogram with all angles equal to 90°.
- Square: A rectangle with all four sides equal.
- Rhombus: A parallelogram with all four sides equal (angles not necessarily 90°).
- Trapezium: Only one pair of opposite sides is parallel.
- Kite: Two pairs of adjacent sides are equal (no parallel sides required).
Types of Quadrilaterals Formula
Properties Summary:
Parallelogram:
- Opposite sides are parallel and equal.
- Opposite angles are equal.
- Diagonals bisect each other (cut each other in half).
Rectangle:
- All properties of a parallelogram.
- All four angles = 90°.
- Diagonals are equal in length.
Square:
- All properties of a rectangle.
- All four sides are equal.
- Diagonals are equal and bisect each other at 90°.
Rhombus:
- All four sides are equal.
- Opposite angles are equal.
- Diagonals bisect each other at 90° (but diagonals are NOT equal).
Trapezium:
- Only one pair of sides is parallel (called parallel sides or bases).
- The other pair is called non-parallel sides or legs.
Kite:
- Two pairs of adjacent sides are equal.
- One pair of opposite angles is equal.
- Diagonals cross at 90°.
Types and Properties
How the types are related:
- A square is a special rectangle (all sides equal) and also a special rhombus (all angles 90°).
- A rectangle is a special parallelogram (all angles 90°).
- A rhombus is a special parallelogram (all sides equal).
- Every square is a rectangle, but not every rectangle is a square.
- Every square is a rhombus, but not every rhombus is a square.
Quick Identification Guide:
- All sides equal + all angles 90° → Square
- Opposite sides equal + all angles 90° → Rectangle
- All sides equal + angles not 90° → Rhombus
- Opposite sides parallel and equal → Parallelogram
- Only one pair of parallel sides → Trapezium
- Two pairs of equal adjacent sides → Kite
Solved Examples
Example 1: Identifying from Properties
Problem: A quadrilateral has all four sides equal and all angles 90°. What type is it?
Solution:
- All sides equal → could be rhombus or square.
- All angles 90° → must be a square.
Answer: It is a square.
Example 2: Identifying a Parallelogram
Problem: ABCD has AB ∥ CD and AD ∥ BC. AB = CD = 7 cm and AD = BC = 5 cm. Angles are not 90°. What type is it?
Solution:
Both pairs of opposite sides are parallel and equal. Angles are not 90°, so it is not a rectangle.
Answer: It is a parallelogram.
Example 3: Identifying a Trapezium
Problem: In quadrilateral PQRS, PQ ∥ SR but PS is not parallel to QR. What type is it?
Solution:
Only one pair of opposite sides (PQ and SR) is parallel.
Answer: It is a trapezium.
Example 4: Identifying a Rhombus
Problem: A quadrilateral has all four sides = 6 cm. Its angles are 60°, 120°, 60°, 120°. Name the shape.
Solution:
- All sides equal → rhombus or square.
- Angles are not 90° → not a square.
Answer: It is a rhombus.
Example 5: Identifying a Kite
Problem: A quadrilateral has sides 5 cm, 5 cm, 8 cm, 8 cm. The equal sides are next to each other (adjacent). Name the shape.
Solution:
Two pairs of adjacent sides are equal (5, 5 and 8, 8).
Answer: It is a kite.
Example 6: True or False
Problem: "Every rectangle is a parallelogram." True or False?
Solution:
A rectangle has both pairs of opposite sides parallel and equal. This is exactly the definition of a parallelogram.
Answer: True. Every rectangle is a special type of parallelogram.
Example 7: True or False (Another)
Problem: "Every parallelogram is a rectangle." True or False?
Solution:
A parallelogram does not need to have 90° angles. So it is not always a rectangle.
Answer: False. A parallelogram is a rectangle only if all its angles are 90°.
Example 8: Real-Life Shape Identification
Problem: Name the type of quadrilateral for each: (a) a book cover, (b) a diamond shape on a playing card, (c) a slice of pizza box flap.
Solution:
- (a) Book cover — opposite sides equal, all angles 90° → Rectangle
- (b) Diamond on a card — all sides equal, angles not 90° → Rhombus
- (c) Pizza box flap — only one pair of parallel sides → Trapezium
Real-World Applications
Quadrilateral shapes in real life:
- Rectangle: Books, doors, screens, tables, football fields.
- Square: Tiles, chess boards, napkins, carrom boards.
- Rhombus: Diamonds in playing cards, kite designs, some road signs.
- Parallelogram: Slanted book holders, some bridges, erasers (side view).
- Trapezium: Bucket (side view), some handbags, lamp shades.
- Kite: Flying kites, some earrings, decorative patterns.
Key Points to Remember
- There are 6 main types of quadrilaterals: parallelogram, rectangle, square, rhombus, trapezium, and kite.
- A parallelogram has both pairs of opposite sides parallel and equal.
- A rectangle is a parallelogram with all angles 90°.
- A square has all sides equal AND all angles 90°.
- A rhombus has all sides equal but angles are not necessarily 90°.
- A trapezium has only one pair of parallel sides.
- A kite has two pairs of equal adjacent sides.
- Every square is a rectangle, but not every rectangle is a square.
Practice Problems
- A quadrilateral has opposite sides parallel, all sides 9 cm, and no right angles. Name the shape.
- Name all the quadrilaterals that have both pairs of opposite sides parallel.
- Is every square a rhombus? Explain.
- A quadrilateral has one pair of parallel sides measuring 10 cm and 6 cm. Name the shape.
- Draw a kite and mark the pairs of equal adjacent sides.
- Fill in: A square is a special case of both a ______ and a ______.
Frequently Asked Questions
Q1. What is the difference between a rhombus and a square?
Both have all four sides equal. But a square also has all angles equal to 90°. A rhombus does not need right angles — its angles can be any value as long as opposite angles are equal.
Q2. Is a rectangle always a parallelogram?
Yes. A rectangle has both pairs of opposite sides parallel and equal, which makes it a parallelogram. But a parallelogram is not always a rectangle because its angles may not be 90°.
Q3. What is a trapezium?
A trapezium is a quadrilateral with exactly one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs.
Q4. Can a shape be both a rectangle and a rhombus?
Yes — that shape is a square! A square has all sides equal (like a rhombus) and all angles 90° (like a rectangle).
Q5. How is a kite different from a parallelogram?
In a kite, two pairs of adjacent (neighbouring) sides are equal. In a parallelogram, opposite sides are equal. Also, a kite does not need any parallel sides.
Q6. How many types of quadrilaterals are there?
The main types studied in school are: parallelogram, rectangle, square, rhombus, trapezium, and kite. These 6 types cover most quadrilateral shapes you will see.
