Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed
Mensuration
Perimeter, area, arcs and sectors, volume and surface area, and the k, k², k³ ladder of similar shapes.
Every lesson here ends the same way: learn it, teach it to an AI pupil who asks the awkward question, then defend it against the thinker with the strongest claim on it — free · no account needed.
4 modules of Pearson Edexcel International GCSE Mathematics, each explained in full — what it is, why it works, when a question is asking for it, the mistakes that cost marks and worked examples — with five graded questions marked on your own device. Completely free.
The modules in Mensuration
Perimeter & Area
Rectangles, triangles, parallelograms, trapezia and compound shapes — with the height rule that separates area marks from area guesses. Perimeter is the distance around; area is the space inside, counted in unit squares.
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. Learn Perimeter & Area →
Circles, Arcs & Sectors
Circumference and area, then the fraction-of-a-circle thinking that turns arcs and sectors into one idea instead of four formulas. Circumference C = 2πr (or πd); area A = πr².
When a question is asking for it: Any circle measurement; 'exact answer' or 'in terms of π' instructions (a decimal there usually loses the final accuracy mark, though method marks can still be earned); and sector questions… Learn Circles, Arcs & Sectors →
Volume & Surface Area
Prisms, cylinders, spheres and cones — filling solids (volume) and wrapping them (surface area), including the formulas the sheet won't give you. Volume fills; surface area wraps.
When a question is asking for it: Capacity and packaging problems; 'how much paint/wrapping' → surface area; 'how much water/concrete' → volume. Learn Volume & Surface Area →
Similar Shapes & Scale Factors
When one shape is an enlargement of another: lengths scale by k, areas by k², volumes by k³ — and how to run those factors in any direction. Similar shapes have the same shape, different size: every length in one is k times the matching length in the other.
When a question is asking for it: Matching sides of similar triangles; 'the areas are 25 cm² and 64 cm²…' (k² given — square-root to reach k); model/map/real problems; and any mixed question hopping between lengths, areas and volumes. Learn Similar Shapes & Scale Factors →
The mistakes that cost marks in Mensuration
One from each module — the error examiners see most, with the module that puts it right.
- Using the slant side as the height. Height is perpendicular to the base — the slant is a trap laid deliberately. (Perimeter & Area)
- Mixing up the formulas: 2πr is the boundary (one r), πr² the area (r squared). Area has the square because it fills 2-D space. (Circles, Arcs & Sectors)
- Cylinder total surface without the two ends: 2πrh is only the wrap; TOTAL adds 2πr². (Volume & Surface Area)
- Scaling area by k: doubling lengths QUADRUPLES area. The carpet for a doubled room costs 4×, not 2×. (Similar Shapes & Scale Factors)
Where Mensuration sits in the specification
Content area 4 of 4MA1, sub-topics 4.9, 4.10, 4.11. Incandio is aligned to the specification and is not published by Pearson; the numbers are given so you can check every module against your own copy.
- 4.9 — Mensuration — circles, arcs, sectors
- 4.10 — 3-D shapes and volume
- 4.11 — Similarity (area and volume factors: Higher)
How Mensuration is mastered on Incandio
Every module above ends the same way: five questions that climb Grade 6 → 9+, then you teach the method back to Ember, an AI pupil who asks the awkward question, and defend it against the mathematician with the strongest claim on it. Exam Ready carries 39 authored exam-style questions across this strand, marked on Incandio.
All of Incandio Mathematics · The 4MA1 specification · Exam Ready