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Understanding Human Behaviour Without Spoken Words

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Understanding Human Behaviour Without Spoken Words — Edwin Ogie Library Understanding Human Behaviour Without Spoken Words Nonverbal Communication as a core human skill — simple, practical, and classroom-friendly. Chapter Objectives Introduction Meaning & Scope Major Channels Interpreting Behaviour Culture & Ethics Practical Applications Case Illustrations Reflection & Practice Summary & Terms By Edwin Ogie Library — clear, usable lessons for students and teachers. Chapter Objectives At the end of this chapter, the reader should be able to: Clearly define nonverbal communication and explain its role in human interaction. Identify and interpret major forms of nonverbal behaviour with accuracy. Analyse behaviour using clusters of cues rather than isolated signals. Apply nonverbal awareness eff...
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Mensuration E-Book & JAMB Mensuration CBT — formulas, worked examples and a responsive practice quiz for students.

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Edwin Ogie Library — Mensuration E-Book & JAMB Mensuration CBT Quiz

Introduction & Key Definitions

Mensuration is the study of measuring lengths, areas, and volumes of geometric figures and solids. Below are the key definitions you need:

  • Perimeter: total distance around a plane figure.
  • Area: measure of the region enclosed by a plane figure.
  • Surface Area: sum of the areas of all faces of a solid.
  • Volume: space occupied by a solid.
  • Arc Length: portion of a circle’s circumference.
  • Chord: straight line joining two points on a circle.
  • Sector: region between two radii and the included arc.
  • Segment: region between a chord and its arc.

Plane Figures — lengths & areas

Triangle

Perimeter = a + b + c
Area = ½ × base × height

Quadrilateral

  • Rectangle: P = 2(l + b), A = l × b
  • Square: P = 4a, A = a²
  • Parallelogram: P = 2(a + b), A = base × height
  • Trapezium: P = sum of sides, A = ½ × h × (sum of parallel sides)
Example 1:

Find the area of a triangle with base 10 cm and height 6 cm.

Area = ½ × 10 × 6 = 30 cm²
Example 2:

Find the perimeter of a rectangle of length 8 cm and breadth 5 cm.

P = 2(8 + 5) = 26 cm

Arcs & Chords

Arc (deg): 2πr × (θ/360)   —   Arc (rad): r × θ

Chord = 2r × sin(θ/2)

Example 3: Arc length of radius 7 cm subtending 60°.
Arc = 2π×7×(60/360) = 7π/3 ≈ 7.33 cm

Sectors & Segments

Sector area = ½ r² θ (radians) or π r² × (θ/360). Segment area = Sector − Triangle area.

Sector diagram

Surface Areas & Volumes

Cuboid TSA = 2(lb + bh + lh)   V = l × b × h

Cylinder TSA = 2πr(r + h)   V = π r² h

Cone TSA = π r (r + l)   V = ⅓ π r² h

Sphere TSA = 4π r²   V = 4/3 π r³

Composite Figures & Earth Distances

Break complex shapes into known solids and sum/subtract volumes or areas as needed.

Great-circle distance (Haversine)

d = 2R · arcsin(√[hav(φ₂−φ₁) + cosφ₁ cosφ₂ · hav(λ₂−λ₁)]) where hav(θ)=sin²(θ/2)

Downloads

Editable and printable resources for study.

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