Chapter 3: Understanding Quadrilaterals — Class 8 Maths Notes

1. What is a Quadrilateral?

A quadrilateral is a polygon with four sides and four vertices. The sum of its interior angles is 360°.

2. Types of Quadrilaterals

Parallelogram: Opposite sides parallel and equal; opposite angles equal; diagonals bisect each other.
Rectangle: Parallelogram with all angles 90°; diagonals equal.
Square: Rectangle + Rhombus (all sides equal & all angles 90°).
Rhombus: All sides equal; diagonals bisect at right angles and bisect angles.
Trapezium (Trapezoid): At least one pair of parallel sides (called bases).
Kite: Two pairs of adjacent equal sides; diagonals perpendicular; one diagonal bisects the other.

Quick visual:

(Draw simple labeled sketches for each: use in-class notes or whiteboard.)

3. Key Properties

Quadrilateral	Important Properties
Parallelogram	Opposite sides equal & parallel; opposite angles equal; diagonals bisect each other.
Rectangle	All angles 90°; opposite sides equal; diagonals equal and bisect each other.
Square	All sides equal; all angles 90°; diagonals equal, perpendicular and bisect angles.
Rhombus	All sides equal; diagonals perpendicular and bisect angles; opposite sides parallel.
Trapezium	One pair of parallel sides (bases); mid-segment = average of bases.
Kite	Two pairs of adjacent equal sides; diagonals perpendicular; one diagonal bisects the other.

Angle sum: For any quadrilateral, interior angles add to 360°. Example: If three angles are 80°, 95°, 120°, the fourth = 360 − (80+95+120) = 65°.

4. Area & Perimeter Formulas

Shape	Perimeter	Area
Rectangle	`2(l + b)`	`l × b`
Square	`4a`	`a²`
Parallelogram	`2(a + b)`	`base × height`
Rhombus	`4a`	`(d1 × d2) / 2` (using diagonals)
Trapezium	`sum of all sides`	`((a + b) / 2) × height` where `a,b` are parallel sides
Kite	`sum of all sides`	`(d1 × d2) / 2` (diagonals)

Note: For some problems you may need to use Pythagoras or trigonometry to find heights or diagonals.

5. Solved Examples

Example 1: Find the area of a rectangle with length 12 cm and breadth 7 cm.

Area = 12 × 7 = 84 cm².

Example 2: A rhombus has diagonals 10 cm and 24 cm. Find its area.

Area = (d1 × d2) / 2 = (10 × 24)/2 = 120 cm².

Example 3: In a parallelogram, base = 15 cm and height = 8 cm. Area = 15 × 8 = 120 cm².

6. Practice Questions (with answers)

Find the perimeter of a square with side 9 cm.
Answer
Perimeter = 4 × 9 = 36 cm.
Diagonal of a rectangle are equal. If l = 5 and b = 12, find diagonal length.
Answer
Diagonal = √(5²+12²)=√169=13
Area of a trapezium with parallel sides 8 cm and 14 cm, height 5 cm.
Answer
Area = ((8+14)/2)×5 = (22/2)×5 = 11×5 = 55 cm²
Sum of three angles of a quadrilateral 100°, 110°, 70°. Find the fourth.
Answer
Fourth = 360 − (100+110+70) = 80°

Try drawing each figure first, label given lengths and mark what you need to find.

7. Tips for Exams

Always label diagrams clearly (sides, heights, diagonals).
Use formulas directly but show working steps — full marks require reasoning.
If height is not given, look for right triangles and use Pythagoras.
Memorize special properties (diagonals of rhombus perpendicular, rectangle diagonals equal etc.).