Geometry and measures

3D shapes, plans and elevations

Q: How many edges does a triangular prism have?

A triangular prism has 9 edges: 3 on each triangular end and 3 joining the ends. It has 5 faces and 6 vertices.

10 past-paper questions, easiest first. Try each one, then reveal the answer.

Foundation & HigherAll 10 from Foundation papers

Revision guide by The Full Marks

3D shapes, plans and elevations: what you need to know

This topic is about describing solids: counting faces, edges and vertices, and drawing what a solid looks like from above (the plan) and from the front and side (the elevations). The questions are short but easy marks to drop through careless counting or drawing the wrong view.

Key facts

A face is a flat surface, an edge is where two faces meet, and a vertex is a corner.
Cube and cuboid: 6 faces, 12 edges, 8 vertices. Triangular prism: 5 faces, 9 edges, 6 vertices.
Square-based pyramid: 5 faces, 8 edges, 5 vertices. A cylinder has 2 flat faces, 1 curved surface and 2 curved edges; a cone has 1 flat face, 1 curved surface, 1 curved edge and 1 vertex; a sphere has 1 curved surface and no edges or vertices.
A prism has the same cross-section all the way through. A pyramid comes to a point (the apex).
For shapes with flat faces: faces $+$ vertices $-$ edges $= 2$ . Use it to check your counts.
Plan = view from above. Front elevation = view from the front. Side elevation = view from the side.

Drawing plans and elevations

Decide which direction you are looking from; the arrow on the diagram tells you.
Imagine the solid squashed flat from that direction and draw the outline, using the real measurements on the grid.
Draw a line wherever there is an edge you would see, such as the ridge of a roof or where two levels meet.
Label lengths if the question asks for them.

Sketching a solid from its plan and elevations

Use the front elevation for the shape of the front face and the plan for the depth.
Read every length carefully from the grid, counting squares rather than guessing.
Sketch the solid in 3D (isometric paper if given) and label its length, width and height.

Worked examples

Example 1 Foundation · grade 1

How many faces, edges and vertices does a square-based pyramid have?

Show the solution

Faces: $1$ square base $+ 4$ triangles $= 5$
Edges: $4$ round the base $+ 4$ up to the top $= 8$
Vertices: $4$ on the base $+ 1$ at the top $= 5$
Check: $5 + 5 - 8 = 2$ ✓

Example 2 Foundation · grade 4

A cylinder has radius $3$ cm and height $8$ cm. It stands upright on its circular base. Describe its plan and its front elevation, with measurements.

Show the solution

From above you see the circular top.
Plan: a circle of radius $3$ cm.
From the front you see the full width (the diameter) and the height.
Front elevation: a rectangle $6$ cm wide and $8$ cm tall.

Common mistakes

Mixing up edges and vertices, or counting only the edges you can see in the picture.
Drawing the front elevation again when the side elevation was asked for.
Leaving out internal lines, such as the ridge line on the plan of a triangular prism or the sloping edges that meet at the top on the plan of a pyramid.
Misreading the grid, so a length on the sketch is one square out. Count the squares twice.

Exam tips

Use a ruler and the grid squares exactly; plans and elevations on a grid must be drawn to the correct size.
When sketching a solid from its plan and elevations, label the lengths; a correct shape with missing or wrong lengths may not get full marks.

Questions people ask

What is the difference between a plan and an elevation?

A plan is the view looking straight down from above. An elevation is the view from the front or the side, looking horizontally.

How many edges does a triangular prism have?

A triangular prism has $9$ edges: $3$ on each triangular end and $3$ joining the ends. It has $5$ faces and $6$ vertices.

Exam questions: 3D shapes, plans and elevations (10, easiest first)

3D shapes, plans and elevations2 marksGrade 1CalculatorFoundation

November 2023 · Paper 2 Foundation · Q7

Name a pictured solid and sketch a triangular prism.

Show answer

(a)	Cone	1 mark
(b)	A sketch of a prism with two triangular ends joined by three rectangular faces	1 mark

Worked solution Checked against the mark scheme

(a) The solid has a circular base and comes to a point at the top, so it is a cone.

(b) Draw a triangle, draw an identical triangle slightly across and up from it, then join matching corners with three parallel lines.

Watch out: In (b), drawing a square-based pyramid or a flat triangle.

3D shapes, plans and elevations2 marksGrade 1CalculatorFoundation

June 2022 · Paper 3 Foundation · Q9

Count the faces and the edges of a triangular prism.

Show answer

(a)	5	1 mark
(b)	9	1 mark

Worked solution Checked against the mark scheme

(a) Two triangular ends plus three rectangular sides: $2 + 3 = 5$ faces.

(b) Each triangle has 3 edges and three more join the triangles: $3 + 3 + 3 = 9$ edges.

Watch out: Counting vertices (6) instead of edges.

3D shapes, plans and elevations2 marksGrade 1CalculatorFoundation

November 2018 · Paper 3 Foundation · Q5

Name a pictured 3-D solid and count its edges.

Show answer

(a)	Cuboid	1 mark
(b)	$12$	1 mark

Worked solution Checked against the mark scheme

(a) Six rectangular faces, so it is a cuboid.

(b) 4 edges on the top, 4 on the bottom and 4 upright edges: $4 + 4 + 4 = 12$

Watch out: Counting only the edges that can be seen, or confusing edges with vertices (8).

3D shapes, plans and elevations3 marksGrade 1CalculatorFoundation

Specimen · Paper 3 Foundation · Q14

Label an angle in a triangle using three-letter notation, shade a named face of a cuboid and state how many edges a cuboid has.

Show answer

(a)	The angle at B, between BC and BA, marked y	1 mark
(b)	Face CDEG shaded: the long face on the right, between edge DE and edge CG	1 mark
(c)	12	1 mark

Worked solution Checked against the mark scheme

(a) In angle CBA the middle letter, B, is where the angle is. Mark y inside the triangle at B.

(b) Find the four corners C, D, E and G and shade the face they enclose.

Watch out: In (a), marking the angle at C or A instead of the middle letter B.

3D shapes, plans and elevations3 marksGrade 2CalculatorFoundation

November 2023 · Paper 3 Foundation · Q10

Name a five-sided polygon and find the total edge length of a pentagonal prism.

Show answer

(a)	Pentagon	1 mark
(b)	112.5 cm	2 marks

Worked solution Checked against the mark scheme

(a) It has 5 sides, so it is a pentagon.

(b) A pentagonal prism has $5 + 5 + 5 = 15$ edges (two pentagons plus 5 joining edges).

Total length $= 15 \times 7.5 = 112.5$ cm

Watch out: Counting only the edges you can see, or only 10 edges.

3D shapes, plans and elevations3 marksGrade 4CalculatorOn both tiers

June 2024 · Paper 3 Foundation · Q24

Explain why a side elevation of a triangular prism is wrong and draw its plan.

Show answer

(a)	The height should be less than 4 cm (the perpendicular height, $\sqrt7 \approx 2.6$ cm), not the 4 cm sloping edge	1 mark
(b)	A 7 cm by 6 cm rectangle with a line parallel to the 7 cm sides through the middle (3 cm from each side)	2 marks

Worked solution Checked against the mark scheme

(a) Rana drew a 7 cm by 4 cm rectangle. The 4 cm sides of the triangle slope, so the prism is not 4 cm tall. Its height is $\sqrt{4^2 - 3^2} = \sqrt7 \approx 2.6$ cm.

(b) From above you see the 6 cm by 7 cm base. The top edge (ridge) is above the middle of the 6 cm side, so draw a 7 cm by 6 cm rectangle with a line along its length 3 cm from each long side.

Watch out: Leaving out the ridge line in the plan.

3D shapes, plans and elevations3 marksGrade 4CalculatorFoundation

November 2023 · Paper 3 Foundation · Q19

Draw the plan view of a cuboid from its front elevation and its volume.

Show answer

Answer	A rectangle 8 cm by 7 cm	3 marks

Worked solution Checked against the mark scheme

From the elevation the cuboid is 8 cm long and 4 cm high.

Depth $= 224 \div (8 \times 4) = 7$ cm

The plan (view from above) is length × depth: draw a rectangle 8 cm by 7 cm.

Watch out: Drawing the plan as 8 by 4, copying the front elevation.

3D shapes, plans and elevations2 marksGrade 4CalculatorOn both tiers

November 2022 · Paper 2 Foundation · Q19

Draw the side elevation of a solid from its front elevation and plan.

Show answer

Answer	A rectangle 3 squares wide and 5 squares high	2 marks

Worked solution Checked against the mark scheme

Viewed from the right, the width comes from the depth of the plan (3 squares) and the height from the tallest point of the front elevation (5 squares).

Draw a rectangle 3 wide and 5 high. Visible edges where the sloping faces meet appear as horizontal lines across it.

Watch out: Drawing the front elevation again instead of the side view.

3D shapes, plans and elevations2 marksGrade 4CalculatorFoundation

November 2020 · Paper 3 Foundation · Q22

Draw the plan view of a solid made from a pyramid sitting on a cube.

Show answer

Answer	A 6 cm square with both diagonals drawn	2 marks

Worked solution Checked against the mark scheme

From above you see the square top of the cube, 6 cm by 6 cm.

The pyramid's sloping edges meet at the centre, so draw both diagonals of the square.

Watch out: Drawing a front elevation (a triangle on a square).

3D shapes, plans and elevations2 marksGrade 4No calculatorOn both tiers

June 2019 · Paper 1 Foundation · Q25

Sketch the 3D solid shown by a plan and two elevations, labelling its measurements.

Show answer

Answer	Sketch of a cylinder, diameter 4 cm (radius 2 cm), height 5 cm	2 marks

Worked solution Checked against the mark scheme

The plan is a circle, so the solid is round when seen from above.

Both elevations are rectangles, so the solid is a cylinder.

From the grid: diameter 4 cm (radius 2 cm) and height 5 cm.

Watch out: Reading the grid wrongly and labelling the height as 4 cm.

Also tested in these questions

Their main topic is different, but part of each one tests this topic.

June 2023 · Paper 3 Foundation · Q8: Name a quadrilateral from its properties and name a drawn 3D solid.
June 2022 · Paper 1 Foundation · Q22: Read a cylinder's radius and height from a plan and front elevation, then find its volume in terms of pi.
November 2021 · Paper 1 Foundation · Q6: Name a quadrilateral with one pair of parallel sides and name a 3-D solid with two circular ends.