Geometry & Measurement
Angles, Triangles, and Polygons
Types of Angles
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• Acute (< 90°)
• Right (90°)
• Obtuse (90° < angle < 180°)
• Straight (180°)
• Reflex (> 180°)
Angle Rules
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• Angles on a straight line = 180°
• Angles around a point = 360°
• Vertically opposite angles are equal
• Angles in a triangle = 180°
Types of Triangles
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By Sides:
• Equilateral
• Isosceles
• Scalene
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By Angles:
• Acute
• Right-angled
• Obtuse
Pythagoras’ Theorem
• • a² + b² = c²
• • Only for right-angled triangles
• • Example: If a = 3, b = 4, then c = 5
Basic Trigonometry
• • SOHCAHTOA
• • Use with right-angled triangles
• • Find missing sides or angles
Polygons
• • Sum of interior angles: (n - 2) × 180°
• • Regular polygon: Each angle = [(n - 2) × 180°] ÷ n
• • Examples: Triangle, Quadrilateral, Pentagon
Area & Perimeter
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• Square: A = l², P = 4l
• Rectangle: A = l × w, P = 2(l + w)
• Triangle: A = ½ × b × h
• Circle: A = πr², C = 2πr
Volume & Surface Area
• • Cube: V = a³, SA = 6a²
• • Cuboid: V = l × w × h, SA = 2(lw + lh + wh)
• • Cylinder: V = πr²h, SA = 2πr² + 2πrh
Practice Questions
• 1. Find the missing angle: Two angles in a triangle are
60° and 50°.
• 2. Classify a triangle with sides 7 cm, 7 cm, and 5 cm.
• 3. Find the area of a triangle with base 10 cm and
height 5 cm.
• 4. Use SOHCAHTOA to find a missing side.