CORE_MATH • SHS 1Term 3WAEC / WASSCE SyllabusVIP Lesson
Mensuration I: Perimeter & Area of Plane Shapes
Perimeter and area of triangles, parallelograms, trapeziums, circles, sectors, segments, and composite plane figures.
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Real-World Context & Relevance in Ghana
Building contractors in Tema calculating roofing sheets and floor screeding require precise mensuration of trapezoidal and composite floor plans.
Key Syllabus Learning Objectives
- 1Calculate areas of standard and composite polygons including trapeziums and rhombuses
- 2Determine arc lengths and sector areas of circles given central angles in degrees
- 3Calculate the area of shaded circular segments
- 4Compute the perimeter of composite figures including circular boundaries
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Perimeter of a Sector Caution
Candidates frequently lose marks on perimeter of sector questions by finding only the curved arc length and forgetting to add the two straight radial boundaries (2r).
- Arc length = (θ/360) × 2πr.
- Total perimeter of sector = Arc length + radius + radius = Arc + 2r.
- For a semicircle, Perimeter = πr + 2r.
Core Takeaway:
Always add 2r when asked for the perimeter of any sector.
WAEC / WASSCE Examiner Tips
- Use the exact value of π specified in the examination paper (e.g. "Take π = 22/7" or "π = 3.142"). Do not use your calculator’s internal π button if a specific value is given.
- Always include square units (cm², m²) for area and linear units (cm, m) for perimeter.
- Split composite figures into distinct simple shapes and sum their areas.
Common Candidate Pitfalls & Errors to Avoid
- Forgetting to add 2r to arc length when asked for the perimeter of a sector or semicircle.
- Using slant height instead of perpendicular height in the area of a trapezium or parallelogram.
- Confusing diameter with radius when substituting into πr².
Topic Mastery Checklist
- Can I calculate the area of a trapezium with parallel sides 12 cm and 18 cm, and height 8 cm?
- Can I find the perimeter of a sector of radius 7 cm subtending 60° at the center?
- Can I find the area of a circular segment?
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