📐 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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