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Geometry & Measures · Foundation & Higher

Perimeter & area

Perimeter is the total distance around the outside of a shape. Area is the amount of space enclosed within a shape. Different formulas apply to different shapes.

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Key facts to remember

  • 1Perimeter = sum of all side lengths.
  • 2Area of a rectangle = length × width.
  • 3Area of a parallelogram = base × perpendicular height.
  • 4Area of a trapezium = ½ × (a + b) × h, where a and b are parallel sides.
  • 5Units of area are squared (cm², m²); units of perimeter are linear (cm, m).
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Formulas

Rectangle area
A = l × w
Parallelogram area
A = b × h

h is perpendicular height

Trapezium area
A = ½(a + b)h

a and b are parallel sides

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Worked examples

Example 1

Find the area and perimeter of a rectangle with length 9 cm and width 5 cm.

Working

  1. Area = 9 × 5 = 45 cm²
  2. Perimeter = 2(9 + 5) = 2 × 14 = 28 cm
AnswerArea = 45 cm², Perimeter = 28 cm
Example 2

Find the area of a trapezium with parallel sides 8 cm and 5 cm, and height 4 cm.

Working

  1. A = ½ × (a + b) × h
  2. A = ½ × (8 + 5) × 4
  3. A = ½ × 13 × 4 = 26 cm²
Answer26 cm²
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Common mistakes

✗Confusing perimeter (length) with area (length²) and using the wrong units.
✗Using the slant height instead of the perpendicular height in area formulas.
✗Forgetting to halve in the trapezium formula.
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Exam tips

✓Always include units in your answer — area needs squared units, perimeter needs linear units.
✓Identify the perpendicular height — it must be at right angles to the base.

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