Quadrilaterals (Grade 5)
A quadrilateral is a closed shape with exactly four sides, four angles, and four vertices. The word comes from quadri (four) and lateral (side).
Quadrilaterals are one of the most common shapes in everyday life. Doors, windows, books, tables, screens, and playing fields are all quadrilaterals. Some have special properties — like all sides equal (rhombus) or all angles 90° (rectangle).
In Class 5, you will learn about different types of quadrilaterals, their properties, and how to identify them based on their sides, angles, and diagonals.
What is Quadrilaterals - Class 5 Maths (Geometry)?
A quadrilateral is a polygon with four sides, four vertices, and four angles. The sum of all interior angles of any quadrilateral is always 360°.
Sum of angles of a quadrilateral = 360°
Types and Properties
| Type | Properties |
|---|---|
| Square | All 4 sides equal, all 4 angles = 90°, diagonals equal and bisect each other at 90° |
| Rectangle | Opposite sides equal and parallel, all 4 angles = 90°, diagonals equal and bisect each other |
| Parallelogram | Opposite sides equal and parallel, opposite angles equal, diagonals bisect each other |
| Rhombus | All 4 sides equal, opposite angles equal, diagonals bisect each other at 90° |
| Trapezium | Exactly one pair of parallel sides (called bases) |
| Kite | Two pairs of adjacent sides equal, one pair of opposite angles equal, diagonals perpendicular |
Relationship between quadrilaterals:
- 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).
Solved Examples
Example 1: Example 1: Identifying a Quadrilateral
Problem: A shape has 4 sides, all equal, and all angles are 90°. Name the quadrilateral.
Solution:
Step 1: All 4 sides equal → could be a rhombus or a square.
Step 2: All angles = 90° → this is a square (a rhombus has equal sides but not necessarily 90° angles).
Answer: Square.
Example 2: Example 2: Finding the Fourth Angle
Problem: Three angles of a quadrilateral are 80°, 90°, and 110°. Find the fourth angle.
Solution:
Step 1: Sum of all angles = 360°.
Step 2: Fourth angle = 360° − (80° + 90° + 110°) = 360° − 280° = 80°.
Answer: The fourth angle is 80°.
Example 3: Example 3: Parallelogram Properties
Problem: In a parallelogram, one angle is 70°. Find all four angles.
Solution:
Step 1: Opposite angles of a parallelogram are equal. So one pair = 70° each.
Step 2: Adjacent angles are supplementary (add up to 180°). So the other pair = 180° − 70° = 110° each.
Answer: The four angles are 70°, 110°, 70°, 110°.
Example 4: Example 4: Perimeter of a Rectangle
Problem: A rectangular garden has length 12 m and breadth 8 m. Find its perimeter.
Solution:
Step 1: Perimeter of a rectangle = 2 × (length + breadth).
Step 2: Perimeter = 2 × (12 + 8) = 2 × 20 = 40 m.
Answer: The perimeter is 40 m.
Example 5: Example 5: Identifying a Trapezium
Problem: A quadrilateral has one pair of parallel sides measuring 10 cm and 6 cm, and the other two sides are 5 cm and 7 cm (non-parallel). What type is it?
Solution:
Step 1: It has exactly one pair of parallel sides.
Step 2: A quadrilateral with exactly one pair of parallel sides is a trapezium.
Answer: Trapezium.
Example 6: Example 6: Rhombus Side Length
Problem: A rhombus has a perimeter of 52 cm. Find the length of each side.
Solution:
Step 1: A rhombus has all 4 sides equal.
Step 2: Each side = Perimeter ÷ 4 = 52 ÷ 4 = 13 cm.
Answer: Each side is 13 cm.
Example 7: Example 7: True or False
Problem: "Every square is a rectangle." True or False?
Solution:
Step 1: A rectangle has opposite sides equal and all angles 90°.
Step 2: A square has all sides equal and all angles 90°.
Step 3: A square satisfies all the conditions of a rectangle (and has an extra property that all sides are equal).
Answer: True. Every square is a rectangle, but not every rectangle is a square.
Example 8: Example 8: Kite Identification
Problem: Priya makes a kite with two pairs of adjacent sides: 15 cm, 15 cm, 25 cm, 25 cm. No sides are parallel. What type of quadrilateral is it?
Solution:
Step 1: It has two pairs of adjacent equal sides (15, 15 and 25, 25).
Step 2: No parallel sides.
Step 3: This matches the definition of a kite.
Answer: Kite.
Example 9: Example 9: Angles Using Variables
Problem: The angles of a quadrilateral are x°, 2x°, 3x°, and 4x°. Find all four angles.
Solution:
Step 1: x + 2x + 3x + 4x = 360°
Step 2: 10x = 360°
Step 3: x = 36°
Step 4: Angles: 36°, 72°, 108°, 144°.
Answer: The four angles are 36°, 72°, 108°, 144°.
Example 10: Example 10: Comparing Shapes
Problem: How many pairs of parallel sides do these have: (a) rectangle, (b) trapezium, (c) kite?
Solution:
(a) Rectangle: 2 pairs (top || bottom, left || right).
(b) Trapezium: 1 pair (the two bases).
(c) Kite: 0 pairs (no sides are parallel).
Real-World Applications
Where do we see quadrilaterals?
- Rectangle: Books, doors, windows, screens, tables, cricket pitches.
- Square: Chess board squares, tiles, carrom boards, handkerchiefs.
- Parallelogram: The cross-section of an eraser, the shape formed by a tilted book.
- Rhombus: Diamond shapes in playing cards, kite bodies, some road signs.
- Trapezium: The shape of a bucket viewed from the side, some handbags, and popcorn tubs.
- Kite: Kites flown during Makar Sankranti, some decorative tiles.
Key Points to Remember
- A quadrilateral has 4 sides, 4 vertices, and 4 angles.
- The sum of interior angles of any quadrilateral is 360°.
- A square has all sides equal and all angles 90°.
- A rectangle has opposite sides equal and all angles 90°.
- A parallelogram has opposite sides equal and parallel, and opposite angles equal.
- A rhombus has all sides equal and opposite angles equal.
- A trapezium has exactly one pair of parallel sides.
- A kite has two pairs of adjacent equal sides.
- Every square is a rectangle, every rectangle is a parallelogram, but not the other way around.
Practice Problems
- Three angles of a quadrilateral are 90°, 85°, and 95°. Find the fourth angle.
- A parallelogram has one angle of 65°. Find all four angles.
- The perimeter of a square is 48 cm. Find the length of each side.
- Name a quadrilateral that has all sides equal but angles are NOT 90°.
- Is every rectangle a parallelogram? Explain.
- A trapezium has parallel sides of 14 cm and 8 cm, and non-parallel sides of 5 cm and 6 cm. Find its perimeter.
- The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find each angle.
- Arjun says every rhombus is a square. Is he correct? Why or why not?
Frequently Asked Questions
Q1. What is a quadrilateral?
A quadrilateral is a closed shape with four straight sides, four vertices, and four angles. Examples include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites.
Q2. What is the angle sum of a quadrilateral?
The sum of the four interior angles of any quadrilateral is always 360°.
Q3. What is the difference between a rhombus and a square?
Both have all four sides equal. A square has all angles of 90°, while a rhombus can have angles other than 90°. Every square is a rhombus, but not every rhombus is a square.
Q4. How is a trapezium different from a parallelogram?
A trapezium has exactly one pair of parallel sides. A parallelogram has two pairs of parallel sides.
Q5. Is a square a rectangle?
Yes. A square meets all the conditions of a rectangle (opposite sides equal, all angles 90°). It is a special rectangle where all four sides are also equal.
Q6. What is a kite in maths?
A kite is a quadrilateral with two pairs of adjacent sides that are equal. It has no parallel sides. One pair of opposite angles are equal, and its diagonals are perpendicular.
Q7. How do you find a missing angle in a quadrilateral?
Add the three known angles and subtract the sum from 360°. For example, if three angles are 80°, 100°, and 90°, the fourth = 360° − 270° = 90°.
Q8. What are the diagonals of a quadrilateral?
Diagonals are line segments connecting opposite vertices. Every quadrilateral has exactly 2 diagonals.
Q9. Can a quadrilateral have all acute angles?
No. If all four angles were less than 90°, their maximum sum would be less than 360°. But the angle sum must be exactly 360°, so at least one angle must be 90° or more.
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Quadrilaterals and their properties are part of the Geometry chapter in the NCERT/CBSE Class 5 Maths curriculum.
Related Topics
- Types of Triangles (Grade 5)
- Circles (Grade 5)
- Lines, Line Segments and Rays
- Parallel and Perpendicular Lines
- Angles (Grade 5)
- Angle Sum Property of Triangle
- Symmetry (Grade 5)
- Reflection and Rotation
- Nets of 3D Shapes (Grade 5)
- Views of 3D Shapes (Grade 5)
- Complementary and Supplementary Angles
- Constructing Triangles
