Perimeter and Area

• Introduction

  • Perimeter: Distance around a closed figure
  • Area: Region covered by a closed figure
  • Standard Units (cm, m, $cm^2$, $m^2$)

• Squares and Rectangles

  • Rectangle
    • Perimeter = $2 \times (length + breadth)$
    • Area = $length \times breadth$
    • Diagonal divides into two equal triangles
  • Square
    • Perimeter = $4 \times side$
    • Area = $side^side$
    • All sides equal

• Parallelograms

  • Base and Height
    • Any side can be a base
    • Height (altitude) is perpendicular to the base
  • Area of Parallelogram = $base \times height$
  • Conversion to rectangle by cutting and shifting

• Triangles

  • Relation to Parallelogram
    • Diagonal divides parallelogram into two congruent triangles
  • Area of Triangle = $\frac{1}{2} \times base \times height$
  • Types of triangles (Right-angled, Equilateral, Isosceles, Scalene)

• Circles

  • Key Components
    • Radius ($r$): Center to boundary
    • Diameter ($d$): Across center ($d = 2r$)
    • Circumference: Perimeter of a circle
  • Pi ($\pi$)
    • Constant ratio ($\frac{\text{Circumference}}{\text{Diameter}} \approx \frac{22}{7}$ or $3.14$)
  • Formulas
    • Circumference ($C$) = $2 \pi r$ or $\pi d$
    • Area of Circle ($A$) = $\pi r^2$

• Conversion of Units

  • Length Conversions
    • $1 \text{ m} = 100 \text{ cm}$
    • $1 \text{ km} = 1000 \text{ m}$
  • Area Conversions
    • $1 \text{ m}^2 = 10,000 \text{ cm}^2$
    • $1 \text{ hectare} = 10,000 \text{ m}^2$

• Applications and Problem Solving

  • Finding path areas inside/outside a field
  • Cost of fencing (using perimeter)
  • Cost of painting/tiling (using area)
  • Composite shapes (combining rectangles, triangles, semicircles)