Use perpendicular height for parallelograms and trapezoids
Calculate parallelogram area · Use the mean of parallel sides for a trapezoid · Match parallel bases with their perpendicular separation
Section Paper 1 · Historical Core · non-calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Rectangle and triangle areas
- Parallel lines
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Calculate parallelogram area
- Use the mean of parallel sides for a trapezoid
- Match parallel bases with their perpendicular separation
Move a triangle to make a rectangle
A parallelogram has area bh: cutting a triangle off one end and moving it to the other makes a rectangle with the same base and perpendicular height. Its sloping side is not generally the height. Its perimeter is 2(base+adjacent side), using actual side lengths.
Pair the parallel sides
A trapezoid with parallel sides a and b and perpendicular separation h has area (a+b)h/2. Two identical copies make a parallelogram with base a+b and height h. Only the parallel sides belong in that average; adding two non-parallel sides does not give the same formula.
Sources for this lesson
Pause and explain
A parallelogram has base 7 cm and perpendicular height 3 cm. What is its area?
Worked example
A trapezoid has parallel sides 5 cm and 9 cm, separated by 4 cm. Find its area.
Show the worked solution
- Mean parallel length = (5+9)/2 = 7 cm.
- Multiply by height 4 cm.
Answer 28 cm².
Try a topic test
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A parallelogram has base 8 cm, adjacent side 5 cm and perpendicular height 4 cm. Find area and perimeter.
Give me a hint
Use height for area and side lengths for perimeter.
Compare my reasoning
- Area = 8×4 = 32 cm².
- Perimeter = 2(8+5) = 26 cm.
32 cm²; 26 cm.
Look for these in your work
- Separate side and height
- Calculate both quantities
A trapezoid has parallel sides 6 m and 10 m and height 3 m. Find its area.
Give me a hint
Average the parallel sides.
Compare my reasoning
- (6+10)/2 = 8 m.
- 8×3 = 24 m².
24 m².
Look for these in your work
- Identify the parallel pair
- Use square units
A trapezoid has area 45 cm² and parallel sides 6 cm and 9 cm. Find the perpendicular separation.
Give me a hint
Rearrange the area equation.
Compare my reasoning
- 45 = (6+9)h/2 = 7.5h.
- h = 45/7.5 = 6 cm.
6 cm.
Look for these in your work
- Use the area condition
- Verify by substitution
Common mistakes
- Use the distance perpendicular to the parallel bases.
- Do not average non-parallel sides.
What can you explain now?
A parallelogram has base 7 cm and perpendicular height 3 cm. What is its area?
Compare with the explanation
21 cm².
Multiply base by perpendicular height.
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Make it stick
A parallelogram has base 7 cm and perpendicular height 3 cm. What is its area?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.