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Is your relationship worth repairing? Get "Build Before You Promise" → Relationship Repair When Love Is Still There but the Relationship Is Falling Apart Sometimes the relationship does not need another argument. It needs two people willing to stop defending themselves long enough to understand what is actually breaking. By Edwin Ogie • Author of The Relationship Repair Handbook , Build Before You Promise , Emotional Mastery , and The Value of You Not every broken relationship is a relationship without love. Sometimes two people still love each other deeply, but they have become exhausted by unresolved arguments, poor communication, resentment, disappointment and repeated misunderstandings. They may still care. They may still want the relationship. They may e...
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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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