Mathematics (4024)
Acute: less than 90° Right angle: exactly 90° Obtuse: between 90° and 180° Straight line: 180° Reflex: between 180° and 360°
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°
Rectangle: A = length × width Triangle: A = ½ × base × height Circle: A = πr² Trapezium: A = ½(a+b)h Parallelogram: A = base × height
Perimeter: add up all sides Circle circumference: C = 2πr = πd
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:
Angle Rules:
Area Formulae:
Perimeter & Circumference:
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!