Quadrilaterals & Polygons

Quadrilaterals और Polygons — properties से marks

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Quadrilaterals & Polygons

  • Geometry
  • Quadrilaterals & Polygons
Hello दोस्तों! MeraExam की एक और class में आपका स्वागत है। आज का topic है — Quadrilaterals और Polygons — properties से marks। मैं promise करती हूँ, आज के बाद ये topic आपको आसान लगेगा। शुरू करें?
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Learning Objective

Recall properties of square, rectangle and rhombus, and use (n − 2) × 180° for polygon angles.

🎯 Learning Objective

Recall properties of square, rectangle and rhombus, and use (n − 2) × 180° for polygon angles.

💡 Concept

  • Square: all sides equal; diagonals equal, perpendicular bisectors; diagonal = a√2
  • Rectangle: diagonals equal and bisect each other; diagonal = √(l² + b²)
  • Rhombus: all sides equal; diagonals UNEQUAL but perpendicular bisectors; side² = (d₁/2)² + (d₂/2)²
  • Angle sum of any quadrilateral = 360°
  • Polygon interior angle sum = (n − 2) × 180°; each exterior angle of a regular polygon = 360°/n

🧮 Key Formulas

Interior angle sum = (n − 2) × 180°

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Each exterior angle (regular) = 360°/n

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Rhombus: side² = (d₁/2)² + (d₂/2)²

✏️ Easy Example

Q. Find the sum of the interior angles of a hexagon.

  1. n = 6
  2. Sum = (6 − 2) × 180
  3. = 4 × 180

Answer: 720°

🇮🇳 Real-Life Example

A carrom board is a square — equal diagonals crossing at 90° at the centre circle — while a flying kite (पतंग) shows unequal perpendicular diagonals.

📝 Exam-Level Example

Q. Each interior angle of a regular polygon is 144°. How many sides does it have?

  1. Exterior angle = 180 − 144 = 36°
  2. n = 360 ÷ 36

Answer: 10 sides

📝 Exam-Level Example

Q. The diagonals of a rhombus are 12 cm and 16 cm. Find its side.

  1. Half diagonals: 6 and 8
  2. side² = 6² + 8² = 100
  3. side = √100

Answer: 10 cm

🪄 Memory Trick

For regular polygons, always jump to the exterior angle: exterior = 180 − interior, then n = 360 ÷ exterior. Two steps, done.

⚠️ Common Mistakes

  • ❌ Using (n − 2) × 180 as EACH angle instead of the total sum
  • ❌ Assuming rhombus diagonals are equal — only square and rectangle have equal diagonals
  • ❌ Forgetting that exterior angles of ANY polygon always total 360°

🏆 Exam Tips

  • ✅ Rhombus side = Pythagoras on HALF diagonals — 6-8-10 style triplets again
  • ✅ Quadrilateral angle questions: three given, fourth = 360 minus their sum

📌 Summary

  • Interior sum = (n − 2) × 180°; exterior sum always 360°
  • Square/rectangle: equal diagonals; rhombus: perpendicular unequal diagonals
  • Rhombus side from half-diagonal right triangle
  • Quadrilateral angles total 360°
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