Perimeter and Area of Plane Figures

Calculate boundary perimeter and flat area of rectangles, squares, triangles, parallelograms, and circles.

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Curated Video Lesson

Visual explanation and practical step-by-step walk-through

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Comprehensive Study Notes

Aligned with Ghana NaCCA & WAEC BECE syllabus standards

Topic Introduction & Real-World Context:

Measurement of boundary lengths (perimeter) and flat surfaces (area) is directly applied in fencing school compounds, tiling classrooms, surveying agricultural land, and tailoring fabrics. In JHS 1, students master the metric units of length and area and calculate perimeters and areas of regular plane figures including rectangles, triangles, and circles.

What You Will Master in This Lesson (NaCCA Objectives):

Distinguish between perimeter (linear distance) and area (two-dimensional surface).

Calculate perimeter and area of squares, rectangles, triangles, and compound shapes.

Calculate the circumference (perimeter) and area of a circle using π = 22/7 or 3.142.

Convert between metric units of length (cm, m, km) and area (cm², m²).

1. Perimeter: Boundary Length

Perimeter is the total continuous distance around the outer boundary of a 2D shape. Units: mm, cm, m, km. • Square: P = 4s (where s is side length). • Rectangle: P = 2(l + w) (length l, width w). • Triangle: P = a + b + c (sum of all 3 sides). • Circle Circumference: C = 2πr or C = πd (radius r, diameter d).

2. Area: Surface Measurement

Area measures the amount of space inside the boundary. Units: cm², m², km². • Square: A = s² (side × side). • Rectangle: A = l × w (length × width). • Triangle: A = ½ × base × perpendicular height = ½bh. • Parallelogram: A = base × perpendicular height = bh. • Trapezium: A = ½(a + b)h (parallel sides a and b, height h). • Circle: A = πr² (where r is radius = diameter / 2).

3. Area of Compound Figures

Compound figures are made of two or more combined basic shapes: Method: 1. Divide the compound figure into non-overlapping rectangles, triangles, or semi-circles. 2. Calculate the area of each individual component shape. 3. Sum the areas together to get the total area.

Common Mistakes Students Make in BECE Examinations:

⚠️Using the slant height of a triangle instead of its perpendicular height for area calculation.

⚠️Using diameter instead of radius in the circle area formula πr².

⚠️Confusing perimeter units (cm) with area units (cm²).

Teacher's BECE Exam Pro-Tips:

⭐Always double-check if diameter or radius is given. If diameter is 14 cm, radius is 7 cm!

⭐When π is given as 22/7, check if radius is a multiple of 7 to cancel out denominators.

⭐Include correct units in your final answer (cm or cm²).

Quick Revision Summary Checklist:

Perimeter = distance around boundary.

Rectangle: P = 2(l + w), Area = l × w.

Triangle: Area = ½ × base × height.

Circle: Circumference = 2πr; Area = πr².

Step-by-Step Worked Examples (1)

Real BECE exam-standard problems with complete solution steps

Example 1: Area and Circumference of a Circle

Problem StatementA circular garden has a diameter of 14 m. Taking π = 22/7, find its: (i) circumference (ii) area.

Step-by-Step Solution:

Step 1: Radius r = diameter / 2 = 14 / 2 = 7 m.

Step 2: Circumference C = 2πr = 2 × (22/7) × 7 = 44 m.

Step 3: Area A = πr² = (22/7) × 7 × 7 = 154 m².

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Key Takeaway / Exam Rule: Always find the radius first by halving the diameter before calculating area.

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