Mensuration, Symmetry & Data Handling

1. Mensuration (Perimeter and Area)

Perimeter

The DISTANCE AROUND a closed shape. Think: the FENCE around a field.

ShapePerimeter Formula
Square4 × side
Rectangle2 × (Length + Width)
TriangleSum 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).

ShapeArea Formula
Squareside × side = s²
RectangleLength × Width
Triangle½ × base × height
Circleπr²

Practice

  1. A square field has side 15 m. Perimeter? (60 m). Area? (225 m²)
  2. A rectangle is 10 m long, 6 m wide. Perimeter? (32 m). Area? (60 m²)
  3. 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

  1. Collect: Survey, measure, count
  2. Organise: Tally marks, frequency table
  3. 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

SubjectStudents
Math12
Science10
English8

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.

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