2D and 3D shapes
Naming flat shapes and solids, counting faces, edges and vertices, nets, symmetry and circles: the facts to know, the quick way to use them, and the traps the wrong answers set.
Chapter 1
What are 2D and 3D shapes questions?
Shape questions test facts about flat shapes and solids: what a shape is called, what makes it that shape, and how many faces, edges, corners or lines of symmetry it has.
The shape. Named in words, described by what it has, or drawn.
What it asks. A name, a count, or which shape fits the clues.
Which solid has 7 faces and 12 edges?
The options
- Option 1: cuboid
- Option 2: cube
- Option 3: hexagonal pyramid
- Option 4: pentagonal prism
A Maths question from Rush, level 3.
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Faces, edges and vertices
Faces are the flat surfaces. Edges are the lines where two faces meet. Vertices are the corners (one is a vertex). A cube has 6 faces, 12 edges and 8 vertices.
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Prisms and pyramids
A prism has the same shape at both ends, joined by rectangles. A pyramid has one base, with triangles that meet at a point. The name gives the end or base: a triangular prism, a square-based pyramid.
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- tri3
- quad4
- penta5
- hexa6
- hepta7
- octa8
- nona9
- deca10
- dodeca12
The number is in the name
A polygon is a flat shape with straight sides, and it has as many corners as sides. Regular means every side and angle match, so a regular octagon with 5 cm sides measures 8 × 5 = 40 cm round.
Chapter 2
Solve it in 3 steps.
Here’s the question, one step at a time.
The question
Which solid has 7 faces and 12 edges?
The options
- Option 1: cuboid
- Option 2: cube
- Option 3: hexagonal pyramid
- Option 4: pentagonal prism
A Maths question from Rush, level 3.
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Step 1
Turn the faces into a base.
A prism has its 2 ends and a rectangle for each side of the end. A pyramid has its base and a triangle for each side of the base. So 7 faces is a prism with 5‑sided ends (5 + 2) or a pyramid on a 6‑sided base (6 + 1).
5 + 2 = 7 faces 6 + 1 = 7 faces -
Step 2
Check the edges.
The prism has 5 edges round each end and 5 joining them: 15. The pyramid has 6 round its base and 6 up to the point: 12. Only the pyramid fits both numbers.
5 + 5 + 5 = 15 6 + 6 = 12 -
Step 3
Name it from its base.
Six sides make a hexagon (hexa means 6), so it’s a hexagonal pyramid. The dashed edges are round the back: hidden, but they still count.
A 6‑sided base: a hexagonal pyramid.
Three mistakes it sets
| Option | Faces | Edges |
|---|---|---|
| cuboid | 6 | 12 |
| cube | 6 | 12 |
| hexagonal pyramid | 7 | 12 |
| pentagonal prism | 7 | 15 |
| The mistake | Do this instead |
|---|---|
| Stopping at the faces. The pentagonal prism has 7 faces too, but 15 edges. | Check every number the question gives. |
| Stopping at the edges. A cuboid has 12 edges, but only 6 faces. | A box always has 6 faces, so 7 rules it out. |
| Picking the cube. A cube is a cuboid with square faces. Its counts are the same: 6, 12 and 8. | Cube and cuboid stand or fall together. Here both fall. |
So it’s the hexagonal pyramid. Both numbers fit a pyramid on a 6‑sided base.
Remember: Faces find the base. Edges check it.
Chapter 3
Solids and their nets.
Shape Facts also draws solids and the flat nets they fold up from. Each card is one kind: the rule, an example and its trap.
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Drawn solids: dashes count
A dashed line is an edge round the back. Count it.
This pentagonal pyramid has 5 edges round its base and 5 up to the point: 10. Trap: 7, the solid lines only. Corners hide too: one sits at the back where dashes meet, so it has 6 vertices, not 5.
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Prism nets: two ends and a strip
Two matching ends, and one rectangle for each side of an end.
Two pentagons and five rectangles fold into a pentagonal prism. Trap: the pentagonal pyramid. A pyramid’s net has triangles round its base, never rectangles.
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Square-based Triangle-based Pyramid nets: base and triangles
One base, with a triangle on every side that folds up to the point.
A square with 4 triangles round it is a square-based pyramid. Trap: four triangles and nothing else is a triangle-based pyramid. Its base is just one more triangle.
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Cuboid Cylinder Boxes and tubes
Six squares make a cube. Any longer rectangle makes it a cuboid.
Trap: “cube” for a cuboid’s net, so check every face is square. Two circles and a rectangle roll into a cylinder. A cone has one flat circle and a point; a sphere has no edges at all.
Chapter 4
Flat shapes.
Naming four-sided shapes and triangles, counting symmetry, and the parts of a circle.
The four-sided family
Parallel sides run the same way and never meet: arrows mark them. Perpendicular lines meet at a right angle: a little square marks it. Each shape lower down is a special case of the one above it, so a square is a rectangle and a rhombus too.
- Trapezium: exactly one pair of parallel sides.
- Kite: two pairs of equal sides, next to each other. 1 line of symmetry.
- Parallelogram: two pairs of parallel sides. Opposite angles match, and neighbours make 180°: 65° has 115° beside it.
- Rectangle: four right angles. 2 lines of symmetry.
- Rhombus: four equal sides. 2 lines, its diagonals.
- Square: both at once. 4 lines.
To name one from clues, start at the top and go down only while every clue fits. Trap: “four right angles and two lengths of side” is a rectangle, not a square.
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Equilateral Isosceles Scalene Triangles: what matches?
All three sides match, two, or none. Equal angles mean equal sides.
Angles of 47°, 47° and 86°: two match, so it’s isosceles. None is 90° or more, so it isn’t right-angled or obtuse-angled. Trap: scalene, because no sides were given.
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Rectangle: 2 Regular hexagon: 6 Lines of symmetry: fold it
Fold it in your head: down, across and corner to corner.
A rectangle folds down and across, but corner to corner its corners miss: 2 lines. A regular shape has one line per side. Traps: 4 for a rectangle, and double the right number.
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Start Half turn: it fits Rotational symmetry: turn it
Count how many times it fits its outline in one full turn.
A parallelogram fits after a half turn and again at the end: order 2, though it has no lines of symmetry. A regular hexagon fits 6 times. Trap: 0. Every shape fits once, at the full turn, so the order is at least 1.
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Circles: radius and diameter
A diameter is two radii, through the centre.
A diameter of 26 m means a radius of 13 m. Trap: 52 m, from doubling instead of halving. The circumference is the way round; a chord misses the centre.
Two more kinds in Shape Facts
What fraction is shaded? Shaded over all the parts, then simplify: 6/8 = 3/4. Trap: 1/4, the white part.
Where is the arrow? Find one step first: 100 ÷ 5 = 20. The arrow is one step before 400, so it’s 380. Trap: 400, the nearest label.
Chapter 5: In the exam
Which one is NOT true?
Papers often give a shape and five statements about it, and ask for the one that’s false. Rush doesn’t ask it this way, but the facts above answer it.
Which of these is NOT true for a rhombus?
- A All four sides are equal.
- B Opposite sides are parallel.
- C Opposite angles are equal.
- D It has 4 lines of symmetry.
- E It has rotational symmetry of order 2.
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Step 1
Mark what you know.
A rhombus is a parallelogram with four equal sides. Its ticks and arrows make A and B true, and a parallelogram’s opposite angles match, so C is true.
Equal sides, parallel sides: A, B and C are true.
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Step 2
Fold it, then turn it.
It folds along both diagonals, but not straight down the middle: 2 lines, not 4. So D is false. A half turn fits it, and so does the full turn: order 2, so E is true.
Two lines: its diagonals.
So it’s D. A rhombus has 2 lines of symmetry. 4 belongs to a square.
Remember: Mark it, fold it, turn it.
Other ways the exam asks it
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Can three sides make a triangle?
The two shorter sides must add up to more than the longest. 3 cm and 4 cm make 7 cm, less than 8 cm, so their ends can’t meet.
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Perpendicular on a grid
Count the squares along a line: 3 across and 1 up. A parallel line takes the same steps. A perpendicular one swaps the numbers and turns one round: 1 across and 3 down.
Chapter 6
Try it yourself.
Six real questions from Rush, easy to hard, 60 seconds on the clock.
Use the steps
- Turn the faces into a base.
- Check the edges.
- Name it from its base.
Remember: Faces find the base. Edges check it.
For parents.
What parents ask us about 2D and 3D shapes.
Questions parents ask
What is the difference between a prism and a pyramid?
A prism has the same shape at both ends, joined by rectangles: a triangular prism looks like a tent with a floor. A pyramid has one base with triangles rising to a point. That's why a prism has more faces, edges and corners: it has two ends, while a pyramid has one base and a point.
What are vertices?
They're the corners. One is a vertex, two or more are vertices. A cube has 8 and a square-based pyramid has 5: four round the base and one at the point.
Does my child need to learn all the polygon names?
The ones up to the decagon (10 sides), plus the dodecagon (12). Questions ask both ways round: the name from the number of sides, and the sides from the name. Everyday words share the prefixes: an octopus has 8 arms, and a decade is 10 years.
Is a square a rectangle?
Yes. A rectangle is any four-sided shape with four right angles, and a square is a rectangle whose sides are all equal. It's also a rhombus. If the answer is meant to be 'rectangle' rather than 'square', the question will make that clear: two different side lengths, or exactly two lines of symmetry (a square has four).
Rush: 11+ Practice & KS2 SATsPractise 2D and 3D shapes in Rush.
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