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Not Everything That Stops Working Has Lost Its Value

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Not Everything That Stops Working Has Lost Its Value Feeling broken by life's setbacks? Discover why your value never decreases because of failure, pain, or difficult seasons. Learn the powerful lesson behind the broken machine and why your worth remains unchanged. The Broken Machine That Changed Everything Imagine walking into a workshop and finding an old industrial machine covered in dust and rust. It has not worked for years. Most people pass it without a second thought. "It is finished." "It is useless." "It belongs in the scrapyard." Those are the words many would use. Then an experienced engineer enters. Instead of seeing a useless machine, he sees possibility. He opens the casing, examines the internal parts, replaces a few worn components, reconnects the wiring, and powers it on. Within moments, the machine is running again. What changed? Not its value. Only its condition. That simple scene teaches one of the most important lessons about human...
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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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