Geometry Basics – Quick Study Notes
(For Delhi Police Sub‑Inspector (SI) Quantitative Aptitude)
Goal – Know the what and how of basic geometry.
The notes are written in plain English, short sentences, and everyday analogies.
1. What is Geometry?
Geometry is the study of shapes, sizes, and space.
Think of it as drawing the world around you – a door, a pizza slice, a round clock.
2. Basic Shapes & Their “Names”
| Shape | Everyday Analogy | Key Feature |
|---|---|---|
| Line | A straight stick | No width, only length |
| Line segment | A ruler | Endpoints exist |
| Angle | Two meeting sticks | Measured in degrees |
| Triangle | Pizza slice | 3 sides |
| Quadrilateral | Doorframe | 4 sides |
| Rectangle | Door | Opposite sides equal |
| Square | Checkerboard tile | All sides equal |
| Circle | Clock face | All points same distance from center |
3. Angles – The “How Big” Part
| Symbol | What it means | Everyday Analogy |
|---|---|---|
| ∠ | Angle | The corner of a book |
| 90° | Right angle | A corner of a room |
| 180° | Straight line | A straight road |
| 360° | Full turn | A spinning wheel |
Tip: Add the numbers of three angles in a triangle → 180°.
4. Perimeter – “Walking Around”
The perimeter is the total distance around a shape.
| Shape | How to find |
|---|---|
| Rectangle / Square | 2 × (length + width) |
| Triangle | Sum of the three sides |
| Circle | 2 × π × radius (≈ 6.28 × radius) |
Example:
A door is 2 m wide and 2.5 m tall.
Perimeter = 2 × (2 + 2.5) = 9 m.
5. Area – “Covering the Surface”
Area tells you how much space a shape covers.
| Shape | Formula (plain) | Example |
|---|---|---|
| Rectangle / Square | length × width | 4 m × 5 m → 20 m² |
| Triangle | ½ × base × height | 6 m × 4 m → ½ × 6 × 4 = 12 m² |
| Circle | π × radius² | radius = 3 m → 3.14 × 9 ≈ 28.26 m² |
Quick note: π ≈ 3.14, or use 22/7 if you like fractions.
6. Special Triangles (no jargon)
| Triangle | Special Name | Quick Feature |
|---|---|---|
| All sides equal | Equilateral | All angles 60° |
| Two sides equal | Isosceles | Base angles equal |
| Right‑angled | Right triangle | One 90° angle |
Pythagoras (simple):
In a right triangle,
(hypotenuse)² = (leg₁)² + (leg₂)²
Use this to find a missing side.
7. Circle Basics
| Term | Everyday Analogy | Formula (plain) |
|---|---|---|
| Radius | Distance from center to edge | – |
| Diameter | Full width through center | 2 × radius |
| Circumference | Length around circle | 2 × π × radius |
| Area | Covered surface | π × radius² |
Example:
A round table has a radius of 1.2 m.
Circumference ≈ 2 × 3.14 × 1.2 ≈ 7.54 m.
Area ≈ 3.14 × 1.44 ≈ 4.52 m².
8. Quick Conversion
| Shape | Perimeter <-> Area (Typical) |
|---|---|
| Square | If side = 5 m → Perimeter = 20 m, Area = 25 m² |
| Circle | If radius = 3 m → Circumference ≈ 18.84 m, Area ≈ 28.26 m² |
9. Practice Problems (Very Tiny)
-
Triangle – Two sides are 4 m and 5 m, the angle between them is 90°.
What is the area?
Answer: ½ × 4 × 5 = 10 m². -
Rectangle – Length = 7 m, width = 3 m.
Find the perimeter.
Answer: 2 × (7 + 3) = 20 m. -
Circle – Radius = 2.5 m.
Find the area.
Answer: π × 2.5² ≈ 3.14 × 6.25 ≈ 19.63 m².
10. Key Takeaway Cheat Sheet
| Shape | Perimeter Formula | Area Formula |
|---|---|---|
| Square | 4 × side | side² |
| Rectangle | 2 × (L + W) | L × W |
| Triangle | a + b + c | ½ × base × height |
| Circle | 2 × π × r | π × r² |
Remember: