Parallelogram & Rectangle
A parallelogram has both pairs of opposite sides parallel and equal, opposite angles equal, and adjacent angles supplementary (sum 180°). Its diagonals bisect each other but are NOT equal and do NOT meet at right angles. Its area is base × height — never side × side, because the slant side is longer than the perpendicular height. A rectangle is a parallelogram with all angles 90°, so it inherits every parallelogram property AND adds equal diagonals: d = √(l² + b²). The rectangle’s diagonals still bisect each other but are not perpendicular. A CAT favourite is the diagonal-sum law d₁² + d₂² = 2(a² + b²), which links a parallelogram’s diagonals to its sides — handy when only partial data is given. Remember: if you are told the diagonals are equal, the parallelogram must be a rectangle.
✅ Solved examples
✏️ Practice — try these, take hints as needed
📝 Topic test — 8 questions
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Formula Reference Sheet
Area formulas
| Parallelogram | Area = base × height |
|---|---|
| Rectangle | Area = length × breadth |
| Rhombus (diagonals) | Area = ½ × d₁ × d₂ |
| Square | Area = side² = ½ × diagonal² |
| Trapezium | Area = ½ × (a + b) × h |
| Kite | Area = ½ × d₁ × d₂ |
Diagonal & angle properties
| Rectangle diagonal | d = √(l² + b²) |
|---|---|
| Square diagonal | d = side × √2 |
| Rhombus side | side = ½ × √(d₁² + d₂²) |
| Parallelogram angles | adjacent angles sum to 180° |
| Diagonal sum law (parallelogram) | d₁² + d₂² = 2(a² + b²) |