Quadrilaterals (Grade 4)
A quadrilateral is any closed shape with exactly four sides and four angles. Squares, rectangles, and rhombuses are all quadrilaterals.
In Class 4, you will learn to identify and compare different types of quadrilaterals based on their sides, angles, and special properties.
What is Quadrilaterals - Class 4 Maths (Geometry)?
A quadrilateral is a polygon with 4 sides, 4 vertices, and 4 angles. The word comes from quadri (four) and lateral (sides).
The sum of all four interior angles of any quadrilateral is always 360°.
Quadrilaterals (Grade 4) Formula
Sum of angles in a quadrilateral = 360°
Types and Properties
The main types of quadrilaterals are:
| Type | Sides | Angles | Special Properties |
|---|---|---|---|
| Square | All 4 sides equal | All 4 angles = 90° | Opposite sides parallel; diagonals equal and bisect each other at 90° |
| Rectangle | Opposite sides equal | All 4 angles = 90° | Opposite sides parallel; diagonals equal |
| Rhombus | All 4 sides equal | Opposite angles equal | Opposite sides parallel; diagonals bisect each other at 90° |
| Parallelogram | Opposite sides equal and parallel | Opposite angles equal | Diagonals bisect each other |
| Trapezium | One pair of opposite sides parallel | No special angle rule | The parallel sides are called bases |
A square is a special rectangle (all sides equal). A square is also a special rhombus (all angles 90°).
Solved Examples
Example 1: Example 1: Identify the quadrilateral
Problem: A shape has 4 sides, all equal to 5 cm, and all angles are 90°. What is it?
Solution:
Step 1: All 4 sides equal → could be square or rhombus.
Step 2: All 4 angles = 90° → must be a square.
Answer: The shape is a square.
Example 2: Example 2: Rectangle vs square
Problem: Ria's notebook cover has sides of 24 cm and 18 cm. All corners are right angles. What quadrilateral is it?
Solution:
Step 1: Opposite sides equal (24 cm and 18 cm), but not all four sides equal.
Step 2: All 4 angles = 90°.
Answer: It is a rectangle (not a square because length ≠ breadth).
Example 3: Example 3: Identifying a rhombus
Problem: A quadrilateral has all four sides equal to 6 cm. The angles are 60°, 120°, 60°, and 120°. What is it?
Solution:
Step 1: All sides equal → could be square or rhombus.
Step 2: Angles are not all 90° → not a square.
Step 3: Opposite angles are equal (60° and 120°). Check: 60° + 120° + 60° + 120° = 360° ✓
Answer: It is a rhombus.
Example 4: Example 4: Finding a missing angle
Problem: Three angles of a quadrilateral are 80°, 100°, and 90°. Find the fourth angle.
Solution:
Step 1: Sum of all angles = 360°.
Step 2: Fourth angle = 360° − (80° + 100° + 90°) = 360° − 270° = 90°.
Answer: The fourth angle is 90°.
Example 5: Example 5: Parallelogram properties
Problem: A parallelogram has one angle of 70°. Find all four angles.
Solution:
Step 1: In a parallelogram, opposite angles are equal. So one pair = 70° and 70°.
Step 2: Adjacent angles in a parallelogram add up to 180°. So the other pair = 180° − 70° = 110° each.
Step 3: Verify: 70° + 110° + 70° + 110° = 360° ✓
Answer: The four angles are 70°, 110°, 70°, 110°.
Example 6: Example 6: Identifying a trapezium
Problem: A quadrilateral has one pair of parallel sides (top = 4 cm, bottom = 8 cm) and two non-parallel sides (5 cm and 6 cm). What is it?
Solution:
Step 1: Exactly one pair of parallel sides.
Step 2: This matches the definition of a trapezium.
Answer: It is a trapezium.
Example 7: Example 7: Real-life quadrilaterals
Problem: Arjun sees a kite. It has two pairs of adjacent sides that are equal (15 cm, 15 cm, 25 cm, 25 cm). Is a kite a special quadrilateral?
Solution:
Step 1: A kite has two pairs of adjacent (not opposite) sides equal.
Step 2: It is a quadrilateral because it has 4 sides.
Answer: Yes, a kite is a special type of quadrilateral with two pairs of equal adjacent sides.
Example 8: Example 8: Sorting shapes
Problem: Sort these into groups — square, rectangle, rhombus, parallelogram, trapezium. Which have all angles 90°?
Solution:
Step 1: Square → all angles 90° ✓
Step 2: Rectangle → all angles 90° ✓
Step 3: Rhombus → opposite angles equal, but not necessarily 90°.
Step 4: Parallelogram → opposite angles equal, but not necessarily 90°.
Step 5: Trapezium → no special angle rule.
Answer: Only square and rectangle always have all angles 90°.
Example 9: Example 9: True or false
Problem: "Every square is a rectangle, but not every rectangle is a square." True or false?
Solution:
Step 1: A square has 4 right angles and opposite sides equal → it meets all rectangle conditions. So every square IS a rectangle. ✓
Step 2: A rectangle can have unequal adjacent sides (e.g., 6 cm × 4 cm). A square requires all sides equal. So not every rectangle is a square. ✓
Answer: True.
Real-World Applications
Quadrilaterals are everywhere:
- Rooms and buildings — floors, walls, and doors are usually rectangles.
- Tiles and bricks — square and rectangular tiles cover surfaces.
- Kites — flying kites are quadrilateral-shaped.
- Diamond shapes on playing cards are rhombuses.
- Road signs — some are rectangular or square.
Key Points to Remember
- A quadrilateral has 4 sides, 4 vertices, 4 angles.
- Sum of all angles = 360°.
- Square: all sides equal, all angles 90°.
- Rectangle: opposite sides equal, all angles 90°.
- Rhombus: all sides equal, opposite angles equal.
- Parallelogram: opposite sides equal and parallel.
- Trapezium: exactly one pair of parallel sides.
- Every square is a rectangle and a rhombus.
Practice Problems
- Name a quadrilateral that has all sides equal but angles are NOT 90°.
- Three angles of a quadrilateral are 70°, 80°, and 110°. Find the fourth angle.
- A parallelogram has one angle of 55°. Find the other three angles.
- How is a square different from a rhombus?
- Aditi draws a shape with one pair of parallel sides. The parallel sides are 10 cm and 6 cm. Name the shape.
- List all quadrilaterals that have both pairs of opposite sides parallel.
- Draw a rectangle and a square. Measure the diagonals of each. What do you notice?
Frequently Asked Questions
Q1. What is a quadrilateral?
A quadrilateral is a closed shape with exactly 4 straight sides, 4 vertices, and 4 angles. Examples include squares, rectangles, rhombuses, parallelograms, and trapeziums.
Q2. What is the sum of angles in a quadrilateral?
The sum of all four interior angles of any quadrilateral is always 360°.
Q3. How is a rectangle different from a parallelogram?
Both have opposite sides equal and parallel. The key difference is that a rectangle has all angles equal to 90°, while a parallelogram may have angles other than 90°.
Q4. Is a square a rectangle?
Yes. A square has all the properties of a rectangle (opposite sides equal, all angles 90°) plus the extra property that all four sides are equal.
Q5. 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.
Q6. What is the difference between a rhombus and a square?
Both have all four sides equal. The difference is that a square has all angles at 90°, while a rhombus can have angles other than 90°. A square is a special rhombus.
Q7. Can a quadrilateral have all four sides of different lengths?
Yes. A quadrilateral with all four sides of different lengths and no parallel sides is simply called an irregular quadrilateral.
Q8. How many diagonals does a quadrilateral have?
A quadrilateral has exactly 2 diagonals. Each diagonal connects two opposite vertices.
Q9. What is a kite in geometry?
A kite is a quadrilateral with two pairs of adjacent (neighbouring) sides that are equal. Its diagonals cross at right angles.
