Measurement of Plane Figures: Perimeter, Area, Circles, Composite Shapes
What you must be able to do
Know the formulas: rectangle A = ab, P = 2(a + b); parallelogram A = a·h; triangle A = (a·h)/2; trapezoid A = ((a + b)/2)·h; rhombus A = (d₁·d₂)/2. For a circle, C = 2πr and A = πr²; a sector's arc length is (α/360)·2πr and its area (α/360)·πr².
Use consistent units: convert all lengths to the same unit before calculating, and remember that area units convert by the square of the length factor (1 m² = 10 000 cm²).
For composite figures, split the shape into rectangles, triangles and circle parts, or subtract the missing piece from a larger whole. Count only boundary segments for perimeter - interior dividing lines are not part of it.
Traps that appear in questions
- Using the slant side of a parallelogram or trapezoid instead of the perpendicular height.
- Confusing radius and diameter (r = d/2).
- Using π ≈ 3.14 too early and rounding the final answer incorrectly.
- Adding areas when the question asks for perimeter, or vice versa.
- Forgetting that a semicircle's perimeter includes the diameter.
Rule of thumb
Sketch the figure, label the height perpendicular to the base, and write the formula before substituting numbers.
Worked example
A trapezoid has parallel sides 8 cm and 14 cm and height 5 cm. Its area is ((8 + 14)/2)·5 = 11·5 = 55 cm².