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EMOTIONAL MASTERY-PDF - NOW AVAILABLE FOR DOWNLOAD

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⭐ Now Available on Amazon Emotional Mastery A Practical Guide to Self-Control, Confidence, and Mental Strength Stop letting your emotions control you. Learn the proven system to master your inner world and build unshakable mental resilience. ★★★★★ 5.0 out of 5 — 1 Global Rating | Verified Purchase Emotional Mastery A Practical Guide to Self-Control, Confidence, and Mental Strength Edwin Ogie Ken Gullette ✓ Verified Purchase ★★★★★ "A Giant Step Toward Inner Strength" "Edwin Ogie has written a very helpful book that can help you if you have a hard time keeping your emotions balanced. Why do we react the way we do to bad or stressful events? Why do we let people push our buttons? How can we be stronger inside? It isn't easy, but if you read this book and work at the lessons it provides, you might be able to start your journey to a ...
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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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