Class 9 Mathematics - Quadrilaterals (Advanced Notes)

Formulas, Theorems, Diagrams, Solved Questions & Practice Problems

Important Formulas & Properties

ShapePropertiesArea Formula
ParallelogramOpposite sides equal, Opposite angles equal, Diagonals bisect each otherBase × Height
RectangleAll angles 90°, Opposite sides equal, Diagonals equalLength × Breadth
SquareAll sides equal, All angles 90°, Diagonals equal & bisect at 90°Side²
RhombusAll sides equal, Diagonals bisect at 90°(d₁ × d₂) / 2
TrapeziumOne pair of opposite sides parallel(1/2) × (Sum of parallel sides) × Height

Diagrams

Parallelogram Rectangle Trapezium

Key Theorems

Solved Examples

  1. Find the area of a parallelogram with base = 10 cm, height = 6 cm.
    Solution: Area = Base × Height = 10 × 6 = 60 cm².
  2. Find the area of a square of side 8 cm.
    Solution: Area = side² = 8² = 64 cm².
  3. Find the area of a rhombus with diagonals 12 cm and 16 cm.
    Solution: Area = (d₁ × d₂)/2 = (12 × 16)/2 = 96 cm².
  4. Find the area of a trapezium with parallel sides 8 cm and 12 cm, height = 5 cm.
    Solution: Area = 1/2 × (8+12) × 5 = 50 cm².
  5. In a rectangle, length = 15 cm, breadth = 10 cm. Find perimeter.
    Solution: Perimeter = 2 × (l + b) = 2 × (15 + 10) = 50 cm.

Practice Questions

  1. Find the area of a parallelogram with base 12 cm and height 7 cm.
  2. Find the perimeter of a square of side 9 cm.
  3. Find the area of a rectangle with length 14 cm and breadth 6 cm.
  4. Find the area of a trapezium with parallel sides 10 cm and 14 cm, height = 8 cm.
  5. Find the area of a rhombus with diagonals 10 cm and 8 cm.
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