Mensuration

• Introduction to Mensuration
  • Definition: Branch of mathematics dealing with geometrical figures and their measurement.
  • Applications: Calculating distance, area, and volume in daily life.
• Closed Figures
  • Definition: Figures that start and end at the same point with no breaks.
  • Types: Simple closed curves, polygons, and circles.
• Perimeter
  • Definition: The continuous line forming the boundary of a closed figure.
  • Calculation Method: Sum of the lengths of all the sides.
  • Regular Shapes
    • Equilateral Triangle: $3 \times \text{side}$
    • Square: $4 \times \text{side}$
    • Regular Pentagon: $5 \times \text{side}$
    • Regular Hexagon: $6 \times \text{side}$
  • Irregular Shapes
    • Sum of all outer side lengths.
  • Rectangles
    • Formula: $2 \times (\text{length} + \text{breadth})$
• Area
  • Definition: The amount of surface enclosed by a closed figure.
  • Measurement Unit: Square units (e.g., $\text{cm}^2$, $\text{m}^2$).
  • Estimation Method
    • Using graph paper (counting whole squares, half-filled squares, and ignoring smaller ones).
  • Standard Formulas
    • Rectangle: $\text{Length} \times \text{Breadth}$
    • Square: $\text{Side} \times \text{Side}$
• Important Conversions
  • Length
    • $1\text{ m} = 100\text{ cm}$
    • $1\text{ km} = 1000\text{ m}$
  • Area
    • $1\text{ m}^2 = 10,000\text{ cm}^2$