Calculate area and perimeter of plane shapes
Select dimensions for rectangles, triangles, parallelograms and trapeziums, and distinguish perimeter from area.
Use this pathway for Cambridge IGCSE International Mathematics 0607, 2028–2030. Core and Extended objectives are labelled in each lesson; Extended adds requirements beyond Core. Paper 1 and Paper 2 are non-calculator. Papers 3–6 require a graphic display calculator (GDC). These original lessons use self-checked practice; they are not a Cambridge grade, full timed paper or teacher review.
Before you begin
- Check whether your school has entered you for Core or Extended. Core and Extended share most Number ideas, but some notation and methods are Extended only.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which unit is appropriate for area?
What you will learn
- Calculate perimeter by adding boundary lengths
- Find area of rectangles, triangles, parallelograms and trapeziums
- Recall formulas not supplied by Cambridge
Perimeter follows the outside boundary
Add every outside side once. For an area, use square units and the perpendicular height rather than a sloping side where the formula requires height.
Rectangle area is length × width; parallelogram area is base × perpendicular height; trapezium area is half the sum of parallel sides times perpendicular height.
Recall the triangle area formula
Triangle area is 1/2 × base × perpendicular height; Cambridge supplies this formula, but other area formulas in this section are not supplied.
A triangle height meets the base at 90° and may fall outside an obtuse triangle. Identify the matching base and height before substituting.
Pause and explain
Which height belongs in the parallelogram area formula?
Worked example
Find the area of a trapezium with parallel sides 8 cm and 14 cm and perpendicular height 5 cm.
Show the worked solution
- Add the parallel sides: 8 + 14 = 22 cm.
- Area = 1/2 × 22 × 5.
- Area = 55 cm².
Answer 55 cm².
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
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 triangle has base 12 cm and perpendicular height 7 cm. Find its area.
Give me a hint
Use half the base-height product.
Compare my reasoning
- Area = 1/2 × 12 × 7.
- 12 × 7 = 84.
- Half of 84 is 42.
42 cm².
Look for these in your work
- Correct base and height selected
- Triangle factor one-half used
- Square units stated
A rectangle is 8 m by 5 m. Find its perimeter and area.
Give me a hint
Perimeter adds all four sides; area multiplies length by width.
Compare my reasoning
- Perimeter = 8 + 5 + 8 + 5 = 26 m.
- Area = 8 × 5.
- Area = 40 m².
Perimeter 26 m; area 40 m².
Look for these in your work
- All boundary sides counted
- Area formula applied
- Units distinguished
A garden is a 10 m by 6 m rectangle with a 4 m by 2 m corner removed. Find the remaining area and the new perimeter if the removed corner is at the outside and forms a rectangular notch.
Give me a hint
Subtract the cut-out area; for perimeter, replace the two removed boundary pieces with the two new notch edges.
Compare my reasoning
- Original area = 60 m²; notch area = 8 m².
- Remaining area = 60 − 8 = 52 m².
- The cut removes 4 m + 2 m of boundary but adds the same 4 m + 2 m inside, so perimeter remains 32 m.
Remaining area 52 m²; perimeter 32 m.
Look for these in your work
- Area difference calculated
- Notch geometry considered
- Boundary changes accounted
Common mistakes
- Using a sloping side as the perpendicular height
- Adding lengths to find an area
- Forgetting to include every boundary segment in perimeter
- Using linear units for area
What can you explain now?
Find the area of a parallelogram with base 9 cm and perpendicular height 4 cm.
Compare with the explanation
36 cm²
Area = base × perpendicular height.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How do you distinguish a perimeter calculation from an area calculation, and why must height be perpendicular?
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.