Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Perimeter & Area

In one sentence. Rectangles, triangles, parallelograms, trapezia and compound shapes — with the height rule that separates area marks from area guesses.

Mensuration — one of 4 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Euclid. Learn Perimeter & Area, teach it, then defend it against Euclid.

Where this sits in the specification

Specification 4MA1, 4.9 Mensuration of 2-D shapes. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 4.9 — Mensuration of 2-D shapes

1 · Understand it

What it is

Perimeter is the distance around; area is the space inside, counted in unit squares. The formulas: rectangle lw; triangle ½bh; parallelogram bh; trapezium ½(a + b)h. In every one, h means the PERPENDICULAR height — the square-on distance between the parallel sides, never the slanted edge.

Why it works

A parallelogram is a rectangle with a triangle sliced off one end and taped to the other — same area, hence base × perpendicular height. A triangle is half a parallelogram (two copies tile one). A trapezium is half of a parallelogram made by taping a rotated copy to itself — so its area is half of (both parallel sides added) × height. Nothing to memorise blind: each formula is a cutting argument.

When a question is asking for it

Direct area/perimeter questions; compound shapes (split into rectangles and triangles, or subtract a cut-out); and reverse questions ('area is 66, find the height') — the same formula run backwards as an equation.

How to hold it in your head

Area formulas are all secretly 'base × height, sometimes halved'. When a shape is compound, choose between ADDING pieces or SUBTRACTING a hole — whichever needs fewer measurements invented.

2 · The mistakes that cost marks

  • Using the slant side as the height. Height is perpendicular to the base — the slant is a trap laid deliberately.
  • Adding instead of averaging in the trapezium: it's ½(a + b)h, and forgetting the ½ doubles the answer.
  • Confusing perimeter and area — 'how much fence' is perimeter; 'how much grass' is area.
  • In compound shapes, double-counting the shared edge or forgetting that an internal cut adds nothing to area but changes perimeter.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

Find the area of a trapezium with parallel sides 8 cm and 14 cm, and height 5 cm.

  1. Average the parallel sides: (8 + 14)/2 = 11.
  2. Multiply by the height: 11 × 5 = 55.

Answer: 55 cm²

An L-shape is a 8 cm × 5 cm rectangle with a 3 cm × 2 cm rectangle cut from one corner. Find its area.

  1. Full rectangle: 8 × 5 = 40.
  2. Subtract the cut: 3 × 2 = 6.
  3. 40 − 6 = 34.

Answer: 34 cm²

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — A trapezium has parallel sides of 8 cm and 14 cm, and a perpendicular height of 5 cm. Work out its area. (answer in cm²)
  2. Grade 7 — A parallelogram has base 9 cm, slant side 7 cm and perpendicular height 6 cm. Work out its area. (answer in cm²)
  3. Grade 8 — An L-shaped floor is an 8 m × 5 m rectangle with a 3 m × 2 m rectangular corner missing. Work out the floor's area. (answer in m²)
  4. Grade 9 — A trapezium has parallel sides 8 cm and 14 cm, and an area of 66 cm². Work out its perpendicular height. (answer in cm)
  5. 9+ — A square has the same area as a triangle with base 18 cm and height 16 cm. Work out the PERIMETER of the square. (answer in cm)

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Perimeter & Area, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Perimeter & Area works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Perimeter & Area against Euclid — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 10 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

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