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Mensuration of 2D shapes

Revise Mensuration of 2D shapes for Mathematics A 4MA1 (O Level) — revision notes, 236 practice questions and instant AI marking.

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  Pearson Edexcel International GCSE Mathematics A (4MA1)

Mensuration of 2D shapes

The big idea: Perimeter is a length, area is a length times a length. Keep that straight and you will never square a perimeter or forget to square a conversion factor.

Summary — What This Chapter Covers
  • Convert metric lengths and areas: 1 m2 = 10 000 cm2, 1 cm2 = 100 mm2.
  • Perimeter is the total distance round the outside; area is the space inside.
  • Triangle ½bh; rectangle lw; parallelogram bh; trapezium ½(a + b)h (given).
  • Circle: C = πd = 2πr and A = πr2 (memorise); semicircles are half of each, plus the diameter for the perimeter.
  • Higher: arc length and sector area are a fraction θ/360 of the full circle.
1. Metric Units of Length and Area
Foundation & Higher

Square the conversion factor

Lengths: 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km. For areas the factor is squared, because a square of side 1 m is 100 cm by 100 cm.

Area units 1 cm2 = 10 × 10 = 100 mm2    1 m2 = 100 × 100 = 10 000 cm2
Worked Example

Convert (a) 3.5 m2 to cm2, (b) 4500 mm2 to cm2.

2. Triangles, Rectangles and Compound Shapes
Foundation & Higher

Perimeter and area

Split a compound shape into rectangles and triangles, or take a piece away from a larger rectangle. For perimeter, find every missing side first and then go all the way round.

Areas (memorise) rectangle = length × width    triangle = ½ × base × perpendicular height
Worked Example

An L-shape is made by removing a 4 cm by 3 cm rectangle from one corner of a 10 cm by 8 cm rectangle. Find its area and perimeter.

3. Parallelograms and Trapezia
Foundation & Higher

Perpendicular heights

Both use the perpendicular height, at right angles to the base — never the sloping side.

Areas parallelogram = base × perpendicular height (memorise)    trapezium = ½(a + b)h (given on the formulae sheet)
Worked Example

A trapezium has parallel sides 6 cm and 10 cm, 4 cm apart. Find its area.

Practice Question 1

A parallelogram has base 9 cm, sloping side 6 cm and perpendicular height 5 cm. Find its area.

4. Circles and Semicircles
Foundation & Higher

Circumference and area

These formulae are not on the formulae sheet. Read whether you are given the radius or the diameter. The perimeter of a semicircle is half the circumference plus the straight diameter.

Circle (memorise) circumference = πd = 2πr     area = πr2
Worked Example

A semicircle has diameter 12 cm. Find (a) its area, (b) its perimeter. Give answers correct to 3 significant figures.

5. Sectors of Circles
Higher tier

Arc length and sector area

Memorise
Area units

cm2 → mm2: × 100. m2 → cm2: × 10 000.

Given
Circle

C = πd, A = πr2 — not given.

Sector
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4MA1 Jun 2026 · Paper 1F Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 1F · Variant R Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 1H Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 2H Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 2H · Variant R Edexcel · mark scheme Open → 4MA1 Jun 2026 · Paper 2F Edexcel · mark scheme Open →
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