- Write down the number of faces, edges and vertices of a square-based pyramid.[2]
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Architects and engineers describe 3D objects with flat 2D drawings: a shows the view from directly above, and show the views from the front and the side. Being able to move between a solid and its views — in both directions — is a visual skill that Edexcel tests on isometric grids and squared paper.
The big picture
Each view is a projection: imagine looking straight at the object from one direction and drawing only the outline and edges you would see, with no perspective. A cuboid looks like a rectangle from every direction; a cylinder looks like a circle from above and a rectangle from the side.
Questions range from naming faces, edges and vertices, through drawing the plan and elevations of a solid made of cubes, to working out a solid from its views and finding its volume.
What you'll learn
A is a flat surface, an is where two faces meet, and a is a corner. A cube has 6 faces, 12 edges and 8 vertices.
A has a constant cross-section: a triangular prism has 5 faces, 9 edges and 6 vertices. A has a base and triangular faces meeting at an apex: a square-based pyramid has 5 faces, 8 edges and 5 vertices.
For polyhedra (solids with flat faces), Euler’s formula links them: faces vertices edges .
How many edges does a triangular prism have?
Isometric paper has dots in a triangular pattern, so vertical edges are drawn vertically and horizontal edges run at to the horizontal.
Lengths along the grid lines are true lengths, so a cube of side 2 has edges two dot-spaces long.
Draw visible edges only, and keep the orientation consistent.
Tip — Start isometric drawings from the nearest vertical edge and build outwards. It keeps the shape from skewing.
The is the view from directly above. The is the view from the front, and the is the view from the side (the question will show which side with an arrow).
Draw each view to scale, showing the full outline. Draw internal lines where there is a change in depth or height.
Heights appear in elevations; the plan shows only length and width.
The side view hides detail: from the right you cannot tell that the stacked cube is at the far end. That is why a single view is rarely enough to identify a solid, and why engineers draw three.
Combine the plan (footprint) with the elevations (heights) to reconstruct the solid.
Once the solid is known, find its volume or surface area as usual.
The plan of a solid is a circle and its front elevation is a rectangle. Name the solid.
Think like an examiner
3D shapes
Watch out for these
Stretch yourself
A prism has a cross-section that is a regular hexagon. How many faces, edges and vertices does it have? Check your answer with Euler’s formula.
Hint — A prism has two copies of the cross-section joined by rectangles, one for each side of the cross-section.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 5 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.
A solid is made from centimetre cubes. Its plan is a 3 cm by 2 cm rectangle, and its front and side elevations are rectangles of height 2 cm.
Test yourself
Ready to practise Plans & Elevations? Pick a mode and earn XP & Dobloons.
Real past-paper questions on Plans & Elevations, marked mark-by-mark. How you do feeds straight into your weak-topic list, so your revision keeps targeting what actually needs work.