GCSE Foundation — Geometry and measures
This is the geometry and measures practice for GCSE Foundation, the content area that carries 15% of the paper. The 21 statements below are the whole of geometry and measures for this tier — nothing outside them can be asked, which makes the revision list finite. The list includes geometric terms, notation and diagrams, ruler and compass constructions and loci, angle facts, parallel lines and polygons, properties of triangles and quadrilaterals, congruence criteria for triangles and geometric reasoning and simple proofs. All of it is common to both tiers, so this page is as useful before a Higher paper as before a Foundation one. Only 50% of the paper is straight technique (AO1); 50% asks you to reason, interpret or solve a problem in context, and those marks are won by setting the work out clearly. Much of this is examined on Paper 1, where there is nothing to fall back on but written method.
- G1 — Geometric terms, notation and diagrams
- G2 — Ruler and compass constructions and loci
- G3 — Angle facts, parallel lines and polygons
- G4 — Properties of triangles and quadrilaterals
- G5 — Congruence criteria for triangles
- G6 — Geometric reasoning and simple proofs
- G7 — Transformations: rotation, reflection, translation, enlargement
- G9 — Circle definitions and parts of a circle
- G11 — Geometrical problems on coordinate axes
- G12 — Properties of 3D shapes
- …and 11 more geometry and measures statements at this tier
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Geometry and measures at GCSE Foundation: the 21 DfE statements
Every question on this site is filed against one of these statements. Pick one to practise it on its own.
Sample geometry and measures questions for GCSE Foundation
- A wooden block is a cuboid measuring 2 cm by 10 cm by 15 cm. Work out the volume of the block.(a)27 cm³(b)400 cm²(c)150 cm³(d)300 cm³
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300 cm³ — Method: the volume of a cuboid is length × width × height. Working: 2 × 10 = 20, then 20 × 15 = 300. Answer: 300 cm³. The distractors: 27 cm³ comes from adding the three edges, 2 + 10 + 15, instead of multiplying them; 400 cm² comes from working out the surface area, 2 × (2 × 10 + 2 × 15 + 10 × 15) = 400, which answers a different question and carries a different unit; 150 cm³ comes from multiplying 10 × 15 and leaving the 2 cm edge out of the calculation altogether. - A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.(a)8,000,000 cm³(b)8,000 cm³(c)8 cm³(d)80,000 cm³
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8,000,000 cm³ — Method: change the edge length into centimetres first and then cube it, because 1 m = 100 cm and a volume needs that conversion applied to all three dimensions. Working: 2 m = 2 × 100 = 200 cm, so the volume is 200 × 200 × 200. 200 × 200 = 40,000 and 40,000 × 200 = 8,000,000. Answer: 8,000,000 cm³. The distractors: 8,000 cm³ comes from converting 2 m to 20 cm and cubing that; 80,000 cm³ comes from cubing in metres to get 8 m³ and then multiplying by 10,000, the conversion factor for an area rather than the 1,000,000 a volume needs; 8 cm³ comes from cubing the 2 without converting at all and simply writing cm³ because the question asked for that unit. - A wooden cube has edges of length 4 cm. Work out the total surface area of the cube.(a)96 cm²(b)24 cm²(c)16 cm²(d)64 cm³
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96 cm² — Method: a cube has six identical square faces, so the total surface area is six times the area of one face. Working: one face has area 4 × 4 = 16 cm², and 6 × 16 = 96. Answer: 96 cm². The distractors: 16 cm² is the area of a single face, from stopping before multiplying by the six faces; 64 cm³ comes from working out the volume, 4 × 4 × 4, which is a different measure and carries a different unit; 24 cm² comes from multiplying the six faces by the edge length, 6 × 4, instead of by the area of a face. - A parallelogram has a base of 4 cm and a perpendicular height of 17 cm. Work out the area of the parallelogram.(a)42 cm(b)21 cm(c)34 cm²(d)68 cm²
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68 cm² — Method: the area of a parallelogram is base × perpendicular height. Working: 4 × 17 = 68. Answer: 68 cm². The distractors: 34 cm² comes from halving the product, which is the rule for a triangle and not for a parallelogram; 42 cm comes from treating the two given lengths as the sides of the shape and working out a perimeter, 2 × (4 + 17), which is a length and not an area; 21 cm comes from adding the base and the height, 4 + 17, instead of multiplying them. - A trapezium has parallel sides of 16 cm and 24 cm, and a perpendicular height of 7 cm. Work out the area of the trapezium.(a)280 cm²(b)140 cm²(c)168 cm²(d)47 cm
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140 cm² — Method: the area of a trapezium is the mean of the two parallel sides multiplied by the perpendicular height. Working: (16 + 24) ÷ 2 = 20, then 20 × 7 = 140. Answer: 140 cm². The distractors: 280 cm² comes from multiplying the sum of the parallel sides by the height, (16 + 24) × 7, and forgetting to halve; 168 cm² comes from using only the longer parallel side, 24 × 7, as though the shape were a rectangle; 47 cm comes from adding all three given lengths, 16 + 24 + 7, which gives a length rather than an area.
Frequently asked questions
How much of the GCSE Foundation paper is geometry and measures?
15% of the total marks, and the three papers each carry an equal share of the qualification, so it is spread across all of them rather than concentrated in one.
How many topics are there in geometry and measures at GCSE Foundation?
21 DfE content statements, coded G1 to G25 within this area. Every question in the bank is tagged to one of them.
Is any geometry and measures content on this page Higher only?
No. Foundation pages only show statements a Foundation entry may be asked. The Higher-only geometry and measures material is on the GCSE Higher page for this area.
Can I use a calculator for geometry and measures questions?
Paper 1 is non-calculator; Papers 2 and 3 allow one. Of the 21 statements in this area, 14 are naturally non-calculator and 3 naturally calculator, with the rest workable either way — so practise both.
What kind of marks does geometry and measures carry?
The GCSE Foundation split is 50% AO1 (use and apply standard techniques), 25% AO2 (reason, interpret and communicate) and 25% AO3 (solve problems in and out of context). Questions in this area are set across all three.
Are these past paper questions?
No. Every question at /gcse-foundation is original, written to the DfE content statements and checked before it is published. We do not host past papers or mark schemes.
Do I need an account?
No — you can start practising straight away. Progress is saved automatically in your browser.
Is it free?
Yes. The questions, worked answers and printable worksheets are all free, with no adverts.
Tips for geometry and measures at GCSE Foundation
- Pythagoras' theorem holds only in a right-angled triangle: a² + b² = c², where c is the hypotenuse — the side opposite the right angle and always the longest side.
- To find a shorter side, use the formula the other way round: a² = c² − b², and only take the square root at the end.
- The angles in any triangle add to 180°. In a right-angled triangle the two acute angles add to 90°.
- Perimeter is the distance around the edge (add the sides); area is the space inside, measured in square units. Area of a triangle = ½ × base × height, where the height is perpendicular to the base.
- Volume of a cuboid = length × width × height, in cubic units such as cm³. Convert everything to the same unit before substituting into a formula.
Common mistakes (and how to avoid them)
- Putting the hypotenuse in the wrong place: in a² + b² = c² the side c must be the hypotenuse, opposite the right angle.
- Forgetting the square root at the end — reaching c² = 100 and writing 100 as the answer.
- Working out a² + b² as (a + b)². They are not equal: (a + b)² = a² + 2ab + b².
- Forgetting the ½ in the area of a triangle, or using a sloping side as the height instead of the perpendicular height.
Worked examples
- By Pythagoras: c² = a² + b² = 6² + 8².
- c² = 36 + 64 = 100.
- c = √100 = 10.
- We want a shorter side, so a² = c² − b² = 13² − 5².
- a² = 169 − 25 = 144.
- a = √144 = 12.
- Area = ½ × base × height = ½ × 10 × 6 = 30 cm².
- Volume = length × width × height = 5 × 3 × 4 = 60 cm³.
Geometry and measures is 15% of the Foundation paper, and Pythagoras' theorem is its centrepiece: for the first time you can calculate a length nobody could measure directly, from the diagonal of a screen to the slope of a roof. Remember the three rules — it only works in a right-angled triangle, the hypotenuse is opposite the right angle, and you finish by square-rooting — and pair them with the angle facts and the area and volume formulae. Write the units on every answer, square units for area and cubic units for volume.
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