Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Areas and Perimeters — finding the area and boundary length of rectangles, triangles, trapeziums and compound shapes — to become a reliable source of marks instead of a list of formulas they only half-remember.
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). Examiners expect you to recall standard formulas, split compound shapes into familiar parts, and give answers with correct units.

Key takeaways

• Perimeter is the total distance around a shape; area is the space inside, measured in square units.
• Know the core formulas for rectangle, triangle, parallelogram and trapezium — most compound shapes reduce to these.
• For compound shapes, split or subtract regions rather than guessing a single formula.
• Always state units: cm, m, cm², m² — and convert consistently when a question mixes units.

What are Areas and Perimeters in Cambridge IGCSE Maths?

Areas and Perimeters deal with measuring 2D shapes. Perimeter is found by adding side lengths (or using a formula such as 2(l + w) for a rectangle). Area formulas include base × height for rectangles and parallelograms, ½ × base × height for triangles, and ½(a + b) × h for trapeziums. In Cambridge IGCSE Mathematics, questions often combine several shapes, give algebraic side lengths, or ask you to find a missing dimension when area or perimeter is known.

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
Standard formulas	Rectangle, triangle, parallelogram, trapezium	”Find the area of triangle ABC”
Compound shapes	Split into rectangles/triangles or subtract a hole	”The shape below is made from a rectangle and a semicircle”
Missing dimension	Rearrange area or perimeter formula	”The area is 48 cm². Find the height.”
Unit consistency	Convert before calculating if needed	”Give your answer in m²”

How to find area and perimeter — step by step

The safest method works for every 2D question in this subtopic.

1. Identify the shape — simple or compound. Mark any right angles and parallel sides.
2. Write the correct formula for each part (do not mix perimeter and area formulas).
3. Substitute known lengths. For triangles and parallelograms, use the perpendicular height, not a slanted side.
4. Calculate each part. For compound shapes, add areas or subtract an inner region.
5. Check units — perimeter in linear units, area in square units. 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.

Perimeter vs area: which does the question want?

Students lose marks by adding when they should multiply, or by including internal edges in a perimeter. Use the wording to decide.

Situation	What to do	Typical signal words
Boundary length	Add outer sides only	”perimeter”, “length of fencing”, “border”
Space inside	Use an area formula	”area”, “covered”, “painted”, “turf”
Compound perimeter	Trace the outside; ignore shared internal edges	”perimeter of the shape”
Shape with a cut-out	Subtract inner area from outer	”hole”, “removed”, “shaded region”

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

Most lost marks come from using the wrong formula or the wrong height. 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	Full method with formula stated	”Work out the area of the trapezium.”
Show that	Prove a given result — answer is stated	”Show that the area is 84 cm².”
Write down	Direct recall or one-step result	”Write down the perimeter of the square.”
Give your answer in …	Convert or round as instructed	”Give your answer in m² correct to 2 d.p.”
Form an equation	Use area/perimeter to build algebra	”Form an equation in x and solve.”

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 is 12 cm by 7 cm. Work out its area and perimeter.” Area = 12 × 7 = 84 cm². Perimeter = 2(12 + 7) = 38 cm. Mark-scheme reward: correct formulas and units on both parts.
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 cm². Reward: formula written before substitution on a “Show that” question.
3. “A shape is a 10 cm by 6 cm rectangle with a 2 cm by 2 cm square removed from one corner. Find the area of the remaining shape.” Rectangle area = 60 cm²; removed = 4 cm² → remaining = 56 cm². Reward: subtraction of the hole, not adding extra perimeter edges.

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

Area skills feed directly into Solid Geometry, where the same base-and-height thinking appears in surface area. They underpin Circles when semicircles attach to rectangles, and link to Pythagoras Theorem when you need a perpendicular height. 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 a slanted side as the height of a triangle or parallelogram.
• Including internal edges in the perimeter of a compound shape.
• Forgetting to subtract a removed region when finding shaded area.
• Mixing units — calculating in cm but giving the answer in m² without converting.
• Confusing area and perimeter formulas on the same diagram.

When you need more support

If compound-shape questions keep tripping you up, 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 use the wrong height, confuse perimeter with area, or mishandle compound shapes.

What is the quickest way to tackle a compound shape? Split it into rectangles and triangles you already know, find each area, then add or subtract. Trace only the outside for perimeter.

Do I need to learn the trapezium formula? Yes. Area = ½(a + b) × h, where a and b are the parallel sides and h is the perpendicular distance between them.

How do I revise Areas and Perimeters effectively? Read the subtopic notes, sketch a quick diagram on every question, then take the Areas and Perimeters quiz. Revisit any compound-shape problems you got wrong before moving on.

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