Definition types properties and area formulas of quadrilaterals
The concept of understanding quadrilaterals class 8 is a key part of geometry in the Class 8 Maths curriculum. It helps students identify and differentiate between four-sided figures, study their properties, and solve exam-focused questions quickly and accurately.
What Is Understanding Quadrilaterals?
A quadrilateral is a polygon with four sides, four angles, and four vertices. Understanding quadrilaterals means knowing how to classify various four-sided polygons (such as rectangles, squares, parallelograms, rhombuses, trapeziums, and kites), learning the characteristics of each, and applying formulas for angle calculations, area, and perimeter. You’ll find this concept applied in geometry, mensuration, and even in real-world problems involving shapes and measurements.
Key Formulas for Quadrilaterals
Here are the standard formulas every Class 8 student should remember:
- Angle Sum Property: The sum of all interior angles in any quadrilateral is 360°.
- Perimeter: Add the lengths of all four sides.
- Area: Varies by type:
Rectangle: \( \text{Area} = \text{Length} \times \text{Breadth} \)
Square: \( \text{Area} = \text{Side}^2 \)
Parallelogram: \( \text{Area} = \text{Base} \times \text{Height} \)
Trapezium: \( \text{Area} = \frac{1}{2} \times (\text{Sum of Parallel Sides}) \times \text{Height} \)
Kite/Rhombus: \( \text{Area} = \frac{1}{2} \times \text{Product of Diagonals} \)
Types of Quadrilaterals in Class 8 Maths
| Type | Key Properties | Example |
|---|---|---|
| Rectangle | Opposite sides equal and parallel; all angles are 90°; diagonals equal and bisect each other. | Book, Wall |
| Square | All sides equal; all angles 90°; diagonals equal and bisect at 90°. | Chessboard, Window Pane |
| Parallelogram | Opposite sides equal and parallel; opposite angles equal; diagonals bisect each other. | Slanted Tabletop |
| Rhombus | All sides equal; opposite angles equal; diagonals bisect at right angles. | Diamond, Kite Shape |
| Trapezium | Only one pair of parallel sides. | Bridge, Notebook Stand |
| Kite | Two pairs of adjacent sides equal; one diagonal bisected; one pair of opposite angles equal. | Actual Kite |
| Irregular Quadrilateral | No specific equal sides or parallel sides/angles; any four-sided figure. | Plot Boundary |
Properties of Important Quadrilaterals (Quick Reference Table)
| Property | Rectangle | Square | Parallelogram | Rhombus | Trapezium |
|---|---|---|---|---|---|
| Sides | Opp. equal | All equal | Opp. equal | All equal | 1 pair parallel |
| Angles | All 90° | All 90° | Opp. equal | Opp. equal | Any |
| Diagonals Equal | Yes | Yes | No | No | No |
| Diagonals Bisect Angles | No | Yes | No | Yes | No |
How to Solve Quadrilaterals Questions: Step-by-Step Example
Example: In a quadrilateral, three angles measure 90°, 110°, and 85°. Find the fourth angle.
1. List the given angles: 90°, 110°, and 85°2. Recall the angle sum property: All angles add up to 360°
3. Add the given angles: 90 + 110 + 85 = 285°
4. Subtract from 360° to find the missing angle: 360 − 285 = 75°
Final Answer: The missing angle is 75°.
Speed Trick or Vedic Shortcut
When solving quadrilateral questions in exams:
- If you know three angles, simply subtract their total from 360° to get the fourth.
- For rectangles and squares, remember: Diagonals are always equal.
- In parallelograms, adjacent angles add to 180°.
Practicing these mental shortcuts helps you save precious time in MCQs and written tests. Vedantu’s online classes cover many such tricks and tips with stepwise examples.
Try These Yourself
- Draw a parallelogram and mark all equal sides and angles.
- List the differences between a rectangle and a square in your own words.
- If a trapezium has parallel sides 8 cm and 4 cm, height 5 cm, find its area.
- Identify which of these is NOT a quadrilateral: triangle, rhombus, kite, square.
Frequent Errors and Misunderstandings
- Confusing parallelogram, rhombus, and rectangle properties.
- Forgetting that the sum of all quadrilateral angles is always 360° (not 180° or 720°).
- Mixing up which quadrilaterals have equal diagonals.
- Assuming all quadrilaterals have both pairs of sides parallel (only parallelograms do).
Relation to Other Concepts
The topic of understanding quadrilaterals connects closely to types of quadrilaterals, the angle sum property of quadrilateral, and general concepts of polygons in geometry. It’s also foundational for understanding area and perimeter, as well as for solving problems on area and perimeter of various shapes.
Classroom Tip
A simple way to remember the sum of angles in any quadrilateral is: draw a four-sided figure and split it into two triangles from one vertex. Each triangle has 180°, so 2 × 180 = 360°. Vedantu teachers often demonstrate this with diagrams for better concept clarity.
We explored understanding quadrilaterals class 8—from definition, types, formulas, differences, solved examples, and key mistakes. Keep practicing with Vedantu to master properties and problem-solving in quadrilaterals!
Explore More: Types of Quadrilaterals | Practice Worksheets |
FAQs on Understanding Quadrilaterals in Geometry
1. What is a quadrilateral in geometry?
A quadrilateral is a closed polygon with four sides, four vertices, and four angles. In geometry, quadrilaterals are two-dimensional shapes formed by joining four line segments end to end. The sum of the interior angles of any quadrilateral is always 360°. Common examples include squares, rectangles, parallelograms, rhombuses, trapeziums, and kites.
2. What are the different types of quadrilaterals?
The main types of quadrilaterals are square, rectangle, parallelogram, rhombus, trapezium (trapezoid), and kite. They are classified based on their sides and 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: At least one pair of parallel sides
- Kite: Two pairs of adjacent equal sides
3. What is the sum of interior angles of a quadrilateral?
The sum of the interior angles of a quadrilateral is 360°. This can be understood by dividing a quadrilateral into two triangles. Since each triangle has an angle sum of 180°, we get:
- 2 × 180° = 360°
4. What is the formula for the area of a quadrilateral?
The area of a quadrilateral depends on its type, as there is no single formula for all quadrilaterals. Common formulas include:
- Square: side × side
- Rectangle: length × breadth
- Parallelogram: base × height
- Rhombus: ½ × d₁ × d₂ (diagonals)
- Trapezium: ½ × (sum of parallel sides) × height
5. What is the difference between a square and a rectangle?
The key difference is that a square has all four sides equal, while a rectangle has only opposite sides equal. Both shapes have four right angles (90°).
- Square: All sides equal, diagonals equal and perpendicular
- Rectangle: Opposite sides equal, diagonals equal but not perpendicular
6. How do you find the perimeter of a quadrilateral?
The perimeter of a quadrilateral is the sum of the lengths of all four sides. The formula is:
- Perimeter = a + b + c + d
- Perimeter = 5 + 6 + 7 + 8 = 26 cm
7. 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 add up to 180°
- Diagonals bisect each other
8. What is a trapezium (trapezoid) in geometry?
A trapezium (called trapezoid in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called bases, and the perpendicular distance between them is the height. The area formula is:
- ½ × (sum of parallel sides) × height
9. What are the properties of a rhombus?
A rhombus is a quadrilateral with all four sides equal. Its important properties include:
- Opposite sides are parallel
- Opposite angles are equal
- Diagonals bisect each other at right angles
- Diagonals are perpendicular
10. Can you give an example problem on quadrilaterals?
Yes, here is a simple example using a rectangle. Suppose the length is 10 cm and the breadth is 6 cm.
- Area = length × breadth = 10 × 6 = 60 cm²
- Perimeter = 2(l + b) = 2(10 + 6) = 32 cm
