- Write down the number of faces, edges and vertices of a cuboid.[2]
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G12–G13Geometry & MeasuresFoundation & HigherGrades 2–5
Plans & Elevations
Architects cannot hand builders a 3D model, so they draw flat views instead: the view from above (the ), from the front (the ) and from the side (the ). This lesson covers the faces, edges and vertices of 3D solids and how to move between a solid and its views.
The big picture
Each view flattens the solid by looking straight at it from one direction. Depth disappears, so a view shows only the outline and any edges you would see as lines.
Going backwards — building a solid from its three views — is the harder skill. Each view limits what is possible, and combining all three narrows it down to a single shape, or a small set of possibilities.
What you'll learn
- Identify faces, edges and vertices of 3D solids
- Draw plans and elevations of 3D shapes
- Interpret plans and elevations to describe or sketch a solid
- Use views to calculate volume and count cubes
1
Properties of 3D solids
A is a flat surface, an is where two faces meet, and a is a corner.
Cuboid: 6 faces, 12 edges, 8 vertices. Triangular prism: 5 faces, 9 edges, 6 vertices. Square-based pyramid: 5 faces, 8 edges, 5 vertices.
For these solids, faces vertices edges — a useful check on your counts.
Example 1A pentagonal prism has how many faces, edges and vertices?
1Two pentagon ends plus 5 rectangular sides: 7 faces.
2Each pentagon has 5 edges, plus 5 joining edges: 15 edges.
3Each pentagon has 5 vertices: 10 vertices.
Answer7 faces, 15 edges, 10 vertices (check: )
Your turnSame method, new numbers — try it before moving on.
How many edges does a hexagonal prism have?
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Solution
- 1Two hexagons give edges.
- 2Six edges join the hexagons: .
Answer:
2
Drawing plans and elevations
Plan: look straight down. Front elevation: look from the front. Side elevation: look from the side.
A cylinder standing upright has a circle as its plan and rectangles as both elevations.
A square-based pyramid has a square with its diagonals as its plan, and triangles as its elevations.
Example 1A triangular prism lies with a rectangular face on the ground and its triangular ends facing front and back. Describe its three views.
1From the front you see the triangular end.
2From above you see a rectangle with a line along the ridge.
3From the side you see a rectangle.
AnswerFront elevation: triangle. Plan: rectangle with a central line. Side elevation: rectangle.
Tip — Draw on squared or isometric paper and use the dimensions given — elevations must be to scale.
3
From views to a solid
Match the widths: the plan and front elevation share the same width; the plan and side elevation share the same depth.
For solids made of cubes, the front elevation gives the tallest column in each position across, and the side elevation the tallest in each position front-to-back.
Your turnSame method, new numbers — try it before moving on.
A solid has a circular plan, and its front and side elevations are both triangles. Name the solid.
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Solution
- 1From above it looks like a circle; from the front and side, a triangle.
- 2The solid is a cone.
Answer: cone
Why this works
Two different solids can share the same three views. When a question asks for the "greatest" or "least" number of cubes, it is using that fact.
Think like an examiner
- Label each view clearly as plan, front or side elevation.
- Draw internal edges that can be seen as lines.
- Keep measurements consistent between views.
Remember these
Euler’s formula for these solids.
Volume of a prism.
Views line up.
Watch out for these
Drawing the plan as a 3D sketch.
Every view is a flat 2D shape.
Mixing up front and side elevations.
Use the arrows or labels on the diagram.
Counting hidden edges twice.
Count each edge of the solid exactly once.
Forgetting lines where faces change height.
Show every visible edge in the view.
Stretch yourself
A solid is made from identical cubes. Its plan is a grid of 3 squares across and 2 deep, all filled. The front elevation (3 across) shows column heights 2, 1, 1. The side elevation (2 deep) shows heights 2, 2. Find the number of cubes used.
Hint — Every square in the plan has at least one cube. Only the left column can be 2 tall.
Reveal solution
SolutionThe plan needs at least one cube on each of the 6 squares. The front elevation allows height 2 only in the left column. The side elevation shows height 2 in both the front and back rows, so both left-column squares must be 2 tall. So there are two stacks of 2 and four single cubes: cubes.
Questions students ask
Is the plan always drawn above the front elevation?
Not necessarily in GCSE questions — just label each view.
Does a sphere have edges?
No. It has one curved surface, no edges and no vertices.
What is isometric paper for?
It uses a triangular dot grid so 3D solids can be sketched accurately.
Key takeaways
- Faces, edges and vertices describe 3D solids.
- Plan: from above. Elevations: from the front and side.
- Views are flat 2D drawings to scale.
- Combine all three views to reconstruct a solid.
Exam-style questions
Practise it the way it is examined
3 original questions · 7 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
The front elevation and side elevation of a solid are both rectangles measuring 4 cm by 6 cm. The plan is a square of side 4 cm.
- Name the solid and work out its volume.[3]
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Answer: cm³
- A square-based pyramid has base edges of 6 cm and its apex directly above the centre of the base. Describe its plan view.[2]
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Test yourself
Answer a few questions, then review anything you missed.
Next step
Browse practice topicsKeep practising
Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.