Mathematics (4024)
Topic 4 of 5Cambridge O Levels

Geometry & Angles

Shapes, angles, area and perimeter

Geometry is the study of shapes, sizes, and positions. It's one of the oldest branches of mathematics!


Types of Angles:

  • Acute: less than 90°
  • Right angle: exactly 90°
  • Obtuse: between 90° and 180°
  • Straight line: 180°
  • Reflex: between 180° and 360°

  • Angle Rules:

  • Angles on a straight line = 180°
  • Angles at a point = 360°
  • Vertically opposite angles are equal
  • Angles in a triangle = 180°
  • Angles in a quadrilateral = 360°
  • Interior angles of a polygon = (n-2) × 180°

  • Area Formulae:

  • Rectangle: A = length × width
  • Triangle: A = ½ × base × height
  • Circle: A = πr²
  • Trapezium: A = ½(a+b)h
  • Parallelogram: A = base × height

  • Perimeter & Circumference:

  • Perimeter: add up all sides
  • Circle circumference: C = 2πr = πd

  • Pythagoras' Theorem: a² + b² = c² (where c is the hypotenuse — the longest side of a right triangle)

    Key Points to Remember

    • 1Angles in a triangle = 180°, quadrilateral = 360°
    • 2Area of circle = πr², circumference = 2πr
    • 3Pythagoras: a² + b² = c² (right triangles only)
    • 4Interior angles of polygon = (n-2) × 180°

    Pakistan Example

    Faisal Mosque Architecture

    The Faisal Mosque in Islamabad has a unique triangular design. The main prayer hall is shaped like a desert tent — essentially four large triangles meeting at a peak. Each triangular face has a base of about 60m and a height of 40m. Area of one face = ½ × 60 × 40 = 1,200 m². Four faces = 4,800 m² of outer surface. The minarets are 90m tall — you can use Pythagoras to calculate the diagonal distance from the base of a minaret to its top!

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