Rukasha Maths

GCSE maths Beta

Plans and elevations · Revision guide

Foundation · Geometry · 2 pages in the PDF

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Learning objectives

  • Interpret views of a solid from above, the front and the side.
  • Draw elevations of stacks using the correct viewing direction.

Key ideas

Plan means above: keep width and depth. Front elevation keeps width and height.

A side elevation keeps depth and height. Use the stated side, not a perspective sketch.

For stacks, an elevation uses the greatest height along each line of sight; do not add hidden heights.

A plan shows the footprint. It does not by itself give the number of cubes.

A numbered height plan with back row 1, 3, 1 and front row 2, 1, 0; front heights 2, 3, 1 and right-side heights 2, 3.

Worked examples

Example 1

A cuboid is 5 cm wide, 3 cm deep and 2 cm high. State the dimensions of its three views.

For each view, keep only the two dimensions visible from that direction.

plan:5×3,front:5×2,right side:3×2\text{plan}:5\times3,\quad\text{front}:5\times2,\quad\text{right side}:3\times2
5×3,5×2,3×2(all lengths in cm)5\times3,\quad5\times2,\quad3\times2\quad(\text{all lengths in cm})

Example 2

Stack heights are front row 2, 1, 0 and back row 1, 3, 1, both read left to right. Find the front heights and total cubes.

front heights=(max⁡(2,1),max⁡(1,3),max⁡(0,1))\text{front heights}=(\max(2,1),\max(1,3),\max(0,1))
cubes=2+1+0+1+3+1=8\text{cubes}=2+1+0+1+3+1=8
front heights=(2,3,1),8 cubes\text{front heights}=(2,3,1),\qquad8\text{ cubes}

Watch out

Choose the viewing direction first. An elevation records visible height, not the sum of the cubes behind one another.