📐 Quick Revision Sheet: Geometry for RRB
🔑 Key Concepts (1-liner each)
- Point: No size, only position.
- Line: 1D, endless both ways.
- Ray: Starts at point, endless one way.
- Line-segment: Two fixed ends.
- Angle: Two rays from same point.
- Polygon: Closed figure with ≥3 straight sides.
- Circle: All points equidistant from centre.
| Figure | Area | Perimeter/Circumference |
|---|
| Square (side a) | a² | 4a |
| Rectangle (l×b) | l×b | 2(l+b) |
| Triangle (base b, height h) | ½×b×h | a+b+c |
| Equilateral Δ (side a) | (√3/4)a² | 3a |
| Circle (radius r) | πr² | 2πr |
| Rhombus (diagonals d₁,d₂) | ½ d₁d₂ | 4a |
| Trapezium | ½(a+b)h | sum of 4 sides |
| Parallelogram | base×height | 2(sum of adj. sides) |
Volume & Surface Area (Solids)
| Solid | Volume | TSA | LSA |
|---|
| Cuboid (l×b×h) | lbh | 2(lb+bh+hl) | 2h(l+b) |
| Cube (side a) | a³ | 6a² | 4a² |
| Cylinder (r,h) | πr²h | 2πr(r+h) | 2πrh |
| Cone (r,h) | ⅓πr²h | πr(r+l) | πrl (l=√(r²+h²)) |
| Sphere (r) | 4/3πr³ | 4πr² | — |
⚡ Shortcuts & Tricks
- Right Δ: longest side = hypotenuse; always > each leg.
- Pythagoras: h² = p² + b² → 3-4-5 triple saves 10s.
- Angle sum n-gon: (n-2)×180°.
- Each interior angle of regular polygon: (n-2)×180°/n.
- Circle chord trick: ⊥ from centre bisects chord.
- Tangent rule: radius ⊥ tangent at point of contact.
- Similar Δ: ratio of areas = (ratio of sides)².
- Heron’s Δ area: √[s(s-a)(s-b)(s-c)], s = (a+b+c)/2.
🧠 Memory Aids
- π ≈ 22/7 → “22 July is Pi Day”.
- Pythagoras triplets: 3-4-5, 5-12-13, 8-15-17 (keep in pocket).
- Equilateral Δ area: “Root-3 by 4, side-square no more”.
- Cone volume: “One-third cylinder, ice-cream style”.
- TSA formulas: add ‘2’ for 2-piece solids (cuboid/cylinder), ‘4’ for sphere.
🎯 Common Exam Q&As
Q1. The diagonal of a 12 cm × 5 cm rectangle is?
13 cm (12-5-13 Pythagorean triple)Q2. Area of sector with 60° angle, radius 14 cm (π=22/7)?
θ/360×πr² = 60/360×22/7×14² = 102.67 cm²Q3. How many 3×3×3 cm cubes fit in a 9×9×9 cm cube?
(9/3)³ = 3³ = 27 cubesQ4. Ratio of volumes of two spheres of radii 2 cm & 4 cm?
r³ ratio ⇒ 2³:4³ = 8:64 = 1:8Q5. If each side of a square increases by 10%, area increases by?
1.1² – 1 = 21%
📋 Quick Facts Table
| Fact | Value |
|---|
| Sum of angles in Δ | 180° |
| Sum of angles in quadrilateral | 360° |
| Ext. angle of regular pentagon | 72° |
| π approx. | 22/7 |
| √2 approx. | 1.414 |
| √3 approx. | 1.732 |
| 1 hectare | 10,000 m² |
| 1 acre | 4,047 m² |
🏁 Last-Minute Checklist
Good luck, attempt wisely, guess only if +ve marking!
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