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GCSE/Mathematics/Edexcel

G13Interpret and construct plans and elevations of 3D shapes

Notes

Plans and elevations

Edexcel 1MA1 tests this on Paper 1F and 1H typically. Pupils are given a 3D shape (often built from cubes) and asked to draw its plan and elevations, or to reconstruct the solid from views.

📖DefinitionDefinitions

  • Plan view: looking straight down on the solid (top-down).
  • Front elevation: looking at it from the front.
  • Side elevation: looking at it from one side (usually labelled left or right on the diagram).

Drawing rules

  1. Use squared paper, with one square per cube unit.
  2. Show only what is visible from that direction — no hidden lines, no perspective, no depth.
  3. Outline must be a single closed shape.
  4. Internal "join" lines should be drawn where two faces meet at different depths.

Worked example

A solid made from 4 cubes: 3 in a row at the bottom, 1 cube stacked on the leftmost.

  • Plan: 3 squares in a row (the top of each cube viewed from above).
  • Front elevation: an "L" shape — 3 squares wide, 1 tall, with an extra square stacked on the leftmost.
  • Side elevation: a 1-wide column 2 squares tall (looking from the left side, the stacked cube hides the rest).

Reconstructing from views

When given the three views:

  1. The plan tells you the footprint.
  2. The front elevation tells you the heights at each column position from the front.
  3. The side elevation tells you the heights at each column position from the side.
  4. Cross-reference to determine cube counts at each grid square.

Common Edexcel mark-scheme phrasing

  • B1 each for plan / front / side elevation drawn correctly.
  • M1 for "outline" correct, A1 for "internal lines / joins" correct.
  • B1 for accurate dimensions.

Common mistakesCommon errors

  • Drawing a perspective view instead of a flat 2D projection.
  • Forgetting to mark internal join lines where face depths change.
  • Mixing up front and side elevations (always check which direction the arrow on the diagram points).
  • Drawing the side elevation as a mirror of the front (they are usually different).

AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Practice questions

Try each before peeking at the worked solution.

  1. Question 16 marks

    Plan view of a stacked solid

    Edexcel Paper 1F (non-calculator)

    A solid is made from 5 unit cubes arranged in an L-shape: 3 cubes in a row at the front, with 2 cubes stacked at the back-right.

    (a) Draw the plan view on a square grid. (2 marks)
    (b) Draw the front elevation. (2 marks)
    (c) Draw the right-side elevation. (2 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  2. Question 25 marks

    Reconstruct a solid from views

    Edexcel Paper 1H — Higher

    The plan view of a solid is a 3 × 2 rectangle. The front elevation is a 3 × 2 rectangle. The right-side elevation is a 2 × 2 square.

    (a) Determine the number of unit cubes in the solid. (2 marks)
    (b) Sketch the solid as a 3D shape, showing the dimensions. (3 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

  3. Question 33 marks

    Identify the solid from its views

    Edexcel Paper 1H — Higher

    A solid has:

    • Plan view: a circle.
    • Front elevation: a triangle.
    • Side elevation: a triangle.

    (a) Name the solid. (1 mark)
    (b) The plan diameter is 8 cm and the elevation height is 6 cm. Find the slant height of the solid. (2 marks)

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    AI-generated · claude-opus-4-7 · v3-edexcel-maths-leaves

Flashcards

G13 — Interpret and construct plans and elevations of 3D shapes

7-card SR deck for Edexcel GCSE Mathematics (1MA1) — Leaves Batch 4 topic G13

7 cards · spaced repetition (SM-2)