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.
Put your revision into practice
Choose a topic and try a short quiz with instant explanations. Free, with no signup.
Revising perimeter & area the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Perimeter & area GCSE” on the site for the complete guide.
🔑
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).
📐
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
✍️
Worked examples
Example 1
Find the area and perimeter of a rectangle with length 9 cm and width 5 cm.
Working
Area = 9 × 5 = 45 cm²
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
A = ½ × (a + b) × h
A = ½ × (8 + 5) × 4
A = ½ × 13 × 4 = 26 cm²
Answer26 cm²
⚠️
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.
🎯
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.
Ready to test yourself on Perimeter & area?
Get AI-marked practice questions on exactly this subtopic.