Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Areas and Perimeters — finding the area and boundary length of rectangles, triangles, trapezia and compound shapes — to become a reliable source of marks instead of a list of formulas they mix up.
What query it owns: how to understand and revise Areas and Perimeters in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Areas and Perimeters revision-guide angle, while Tutopiya’s Areas and Perimeters subtopic page owns the learning resource and the free Areas and Perimeters quiz owns the practice.

Areas and Perimeters sit at the heart of the Mensuration unit in Cambridge IGCSE Mathematics (0580/0607). Whenever a question asks for the amount of space inside a 2D shape or the distance around its edge, examiners expect you to pick the correct formula, substitute carefully and give units. This guide explains the shapes and formulas that actually appear, how to split compound figures, and where to practise each skill.

Key takeaways

• Area measures the space inside a shape (cm², m²); perimeter measures the distance around the outside (cm, m).
• Know the standard formulas for rectangle, triangle, parallelogram, trapezium and be ready to apply them in compound shapes.
• For compound shapes, split or subtract regions — never guess a single formula for the whole diagram.
• Always state the formula, show substitution and give the final answer with correct units.

What are Areas and Perimeters in Cambridge IGCSE Maths?

Areas and Perimeters are the two fundamental 2D measurements in Mensuration. Area is the amount of surface enclosed by a shape; perimeter is the total length of its boundary. In Cambridge IGCSE Mathematics they are used to find missing dimensions, compare costs of fencing or paving, and as building blocks for harder Mensuration questions involving circles and solids.

You can read the full explanation, worked examples and notes on Tutopiya’s Areas and Perimeters subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Rectangle	Area = length × width; perimeter = 2(l + w)	“Calculate the area of the rectangle”
Triangle	Area = ½ × base × perpendicular height	”Work out the area of triangle ABC”
Trapezium	Area = ½(a + b) × h (parallel sides a, b)	“Find the area of the trapezium”
Compound shape	Split into known shapes or subtract a hole	”Calculate the shaded area”

How to find area and perimeter — step by step

The safest method works for simple and compound shapes alike.

1. Identify the shape — rectangle, triangle, trapezium or a combination.
2. Write the correct formula before substituting any numbers.
3. Label every dimension on the diagram; find missing lengths if needed.
4. Substitute and calculate; for compound shapes, add or subtract sub-areas.
5. For perimeter, add every outer edge — do not confuse with area formulas.
6. State units: cm² or m² for area; cm or m for perimeter.

Once you have worked through a few, test yourself with the free Areas and Perimeters quiz — it tells you fast whether the method has actually stuck.

Area vs perimeter: which does the question want?

Students lose marks by using an area formula when the question asks for perimeter, or by forgetting to convert units. Use the wording to decide.

Situation	What to do	Typical signal words
Space inside a shape	Use an area formula	”area”, “cover”, “paint”, “turf”
Distance around a shape	Add all outer sides	”perimeter”, “fence”, “border”, “frame”
Compound shaded region	Split or subtract areas	”shaded area”, “cross-section”
Missing dimension	Rearrange the formula	”The area is 48 cm². Work out the length.”

Areas and Perimeters in past-paper wording: command words that matter

Most lost marks come from misreading the command word or picking the wrong formula. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Calculate / Work out	Find area or perimeter with full method	”Work out the area of the trapezium.”
Show that	Prove a given result — the answer is stated	”Show that the area of the shape is 120 cm².”
Write down	State a value; minimal working (usually 1 mark)	“Write down the perimeter of the rectangle.”
Give your answer correct to …	Round as instructed	”Give your answer correct to 2 decimal places.”
Explain	Justify a comparison or choice	”Explain which shape has the greater area.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the formulas — is what method marks reward. Here is how three real-style stems are answered.

1. “A rectangle has length 12 cm and width 7 cm. Calculate the area and the perimeter.” Area = 12 × 7 = 84 cm². Perimeter = 2(12 + 7) = 38 cm. Mark-scheme reward: both formulas stated, correct units on each answer.
2. “A trapezium has parallel sides 8 cm and 14 cm, and perpendicular height 5 cm. Show that its area is 55 cm².” Area = ½(8 + 14) × 5 = ½ × 22 × 5 = 55. Reward: full substitution shown — writing 55 alone scores nothing on “Show that”.
3. “The diagram shows an L-shaped figure. Work out the shaded area.” Split into two rectangles (or one large minus one small), calculate each area, add or subtract. Reward: clear split labelled on the diagram.

When you can recognise the wording instantly, work the full set on the Mensuration topical past paper questions and the Areas and Perimeters quiz to lock the method in.

How Areas and Perimeters connect to the rest of Mensuration

2D area skills feed directly into Circles, where curved boundaries replace straight edges, and into Solid Geometry, where the area of a face becomes a building block for volume and surface area. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Using length × width for a triangle instead of ½ × base × height.
• Confusing area (squared units) with perimeter (linear units).
• Forgetting to convert units before calculating (e.g. metres and centimetres mixed).
• On compound shapes, double-counting a shared edge or missing an outer side for perimeter.
• Rounding too early and losing accuracy marks on multi-step questions.

When you need more support

If area and perimeter questions keep tripping you up — especially compound shapes — work through the Mensuration topical past paper questions and the Areas and Perimeters quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Areas and Perimeters hard in Cambridge IGCSE Maths? No — the formulas are straightforward. Marks are lost when students confuse area with perimeter, use the wrong shape formula, or fail to split compound figures correctly.

What is the quickest way to find the area of a trapezium? Add the two parallel sides, halve the result, then multiply by the perpendicular height: ½(a + b) × h.

How do I find the perimeter of a compound shape? Add only the outer edges — trace around the boundary and include every exposed side. Do not add internal shared edges.

How do I revise Areas and Perimeters effectively? Read the subtopic notes, write the formula before every substitution, then take the Areas and Perimeters quiz. Revisit any compound-shape problems you got wrong before moving on.

Ready to master Cambridge IGCSE Maths Areas and Perimeters?

Start with the Areas and Perimeters subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn Areas and Perimeters into guaranteed marks.

Ready to Excel in Your Studies?

Get personalised help from Tutopiya's expert tutors. Whether it's IGCSE, IB, A-Levels, or any other curriculum — we match you with the perfect tutor and your first session is free.

Book Your Free Trial