Mensuration, Symmetry & Data Handling
1. Mensuration (Perimeter and Area)
Perimeter
The DISTANCE AROUND a closed shape. Think: the FENCE around a field.
| Shape | Perimeter Formula |
|---|---|
| Square | 4 × side |
| Rectangle | 2 × (Length + Width) |
| Triangle | Sum of all 3 sides |
| Circle (Circumference) | 2πr |
Area
The SPACE INSIDE a closed shape. Think: the CARPET on a floor. Measured in SQUARE UNITS (cm², m²).
| Shape | Area Formula |
|---|---|
| Square | side × side = s² |
| Rectangle | Length × Width |
| Triangle | ½ × base × height |
| Circle | πr² |
Practice
- A square field has side 15 m. Perimeter? (60 m). Area? (225 m²)
- A rectangle is 10 m long, 6 m wide. Perimeter? (32 m). Area? (60 m²)
- A circle has radius 7 cm (use π=22/7). Circumference = 44 cm. Area = 154 cm².
2. Symmetry
Line Symmetry (Reflection Symmetry)
A shape has LINE SYMMETRY if it can be FOLDED along a line so that the two halves MATCH EXACTLY. The fold line = LINE OF SYMMETRY.
- Equilateral triangle: 3 lines of symmetry
- Square: 4 lines of symmetry
- Rectangle: 2 lines of symmetry
- Circle: INFINITE lines of symmetry
Mirror Reflection
Your reflection in a mirror is the 'flipped' version. Objects that are SYMMETRICAL look the SAME in a mirror.
3. Data Handling
What Is Data?
Data is INFORMATION — facts, numbers, measurements. We COLLECT data, ORGANISE it, and PRESENT it so it's easy to understand.
Steps
- Collect: Survey, measure, count
- Organise: Tally marks, frequency table
- Present: Pictograph, bar graph
Tally Marks
|||| = 1, 2, 3, 4. |||| = 5.
Bar Graph
A BAR GRAPH uses bars of different HEIGHTS to represent data. The TALLER the bar, the MORE of that item.
Example: Favourite Subjects Survey
| Subject | Students |
|---|---|
| Math | 12 |
| Science | 10 |
| English | 8 |
Draw vertical bars of heights 12, 10, and 8 units.
Pictograph
Uses PICTURES to represent data. Example: 📘 = 5 books.
Practice
Survey your class: 'How do you come to school?' Create a tally chart and a bar graph.
