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GCSE/Mathematics/AQA

G13Interpret and construct plans and elevations of 3D shapes

Notes

Plans and elevations of 3D shapes

A plan and elevations drawing is a 2D representation of a 3D solid from three perpendicular directions. It's essential in technical drawing, architecture and engineering — and a regular GCSE assessment.

Three views

  • Plan view — looking DOWN from above (top view).
  • Front elevation — looking from the FRONT.
  • Side elevation — looking from the SIDE (left or right).

Each view is a flat 2D shape showing what you'd see from that direction, drawn to scale, with hidden edges typically shown as dashed lines.

Worked exampleWorked example: cuboid 4 cm × 3 cm × 2 cm

  • Plan: rectangle 4 cm × 3 cm (looking down).
  • Front elevation: rectangle 4 cm × 2 cm (front face).
  • Side elevation: rectangle 3 cm × 2 cm (side face).

Worked exampleWorked example: triangular prism

  • Plan: rectangle (the base or top).
  • Front elevation: triangle (the end face).
  • Side elevation: rectangle.

Worked exampleWorked example: cylinder (height 6 cm, radius 2 cm)

  • Plan: circle, radius 2 cm.
  • Front elevation: rectangle 4 cm × 6 cm (diameter × height).
  • Side elevation: same rectangle.

Constructing from views

If given plan + front + side, you can reconstruct the 3D shape by overlaying the views.

  • Plan tells you the footprint.
  • Front gives height-and-width.
  • Side gives height-and-depth.

Compound solids (built from cubes)

For shapes built from unit cubes, count carefully. Use grid paper.

Worked example: a shape is 3 cubes long, 2 cubes wide, 1 cube tall, with one extra cube on top of the corner.

  • Plan: a 3 × 2 rectangle with a small square on the top-right.
  • Front: an L-shape — 3 wide, mostly 1 tall but 2 tall on one column.
  • Side: 2 wide, mostly 1 tall but 2 tall on one column.

Common mistakes

  1. Confusing plan with front — plan is always FROM ABOVE.
  2. Drawing the 3D shape itself instead of the 2D views.
  3. Forgetting hidden edges — show with dashed lines if they're behind.
  4. Inconsistent scale between views.
  5. Confusing left and right side elevations — specify which.

Try thisQuick check

A square-based pyramid has its apex directly above the centre of the base. Plan view?

  • A square with diagonals drawn (showing the four edges from base to apex).

AI-generated · claude-opus-4-7 · v3-deep-geometry

Practice questions

Try each before peeking at the worked solution.

  1. Question 12 marks

    Cuboid plan

    (F1) A cuboid is 5 cm × 3 cm × 2 cm (length × width × height). Sketch the plan view and state its dimensions.

    [Foundation tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  2. Question 24 marks

    Cylinder elevations

    (F2) A cylinder has radius 4 cm and height 10 cm. State the shape and dimensions of: (a) plan, (b) front elevation.

    [Foundation tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  3. Question 32 marks

    Triangular prism

    (F3) A triangular prism has a right-angled triangular end (legs 3 cm and 4 cm) and length 10 cm. State the shape of: (a) plan, (b) front elevation.

    [Foundation tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  4. Question 42 marks

    Identify solid from views

    (F/H4) A solid has: plan = circle, front elevation = triangle, side elevation = triangle. Name the solid.

    [Crossover tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  5. Question 52 marks

    Identify solid from views (2)

    (F/H5) A solid has plan = square, front = rectangle, side = rectangle. Name two possible solids.

    [Crossover tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  6. Question 63 marks

    Compound solid plan

    (F/H6) A solid is made from 5 unit cubes: 4 forming a 2×2 base layer, and 1 stacked on the top-left cube. Sketch the plan view and describe it.

    [Crossover tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

  7. Question 73 marks

    Reconstruct from views

    (H7) A solid has: plan = an L-shape (rectangle missing a corner). Front elevation = a rectangle. Side elevation = an L-shape. Describe the solid.

    [Higher tier]

    Ask AI about this

    AI-generated · claude-opus-4-7 · v3-deep-geometry

Flashcards

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

12-card SR deck for AQA GCSE Maths topic G13

12 cards · spaced repetition (SM-2)