Plans and elevations
Maths · GCSE · The School
Three views of one object
A plan is the view looking straight DOWN on a solid. A front elevation is the view looking straight at it from the front, and a side elevation from the side. All three are flat drawings of a three-dimensional object, and the word to hold on to is "straight": you draw what a camera directly above or directly in front would record, with no perspective and nothing hidden behind anything else made smaller. Because they are drawn straight on, every length in a view is a true length, which is what makes the three of them together enough to describe the solid.
Drawing them from the solid
Work on squared paper and keep one scale for all three views. Draw a line wherever the surface changes direction or steps, and nothing where it does not — a smooth face is a blank rectangle, however interesting the object is. A cylinder standing on its end has a circular plan and rectangular elevations; lying on its side it has a rectangular plan and one circular elevation. Line the views up so the front elevation sits directly below the plan and the side elevation beside it: aligned views let you read a height off one and carry it to the other.
Reading a solid back from its views
The harder exam question runs the other way: three views are given and you describe or sketch the solid. Take the plan first, because it fixes the footprint. Then use the front elevation for the height, and the side elevation to check. A square plan with a triangular front elevation and a triangular side elevation is a square-based pyramid. A square plan with a square front and a square side is a cube. Where the two elevations disagree about a height, there is a step in the solid, and that step is what the question is really testing.
A solid is made of a cuboid 4 cm by 3 cm by 2 cm with a 1 cm cube sitting on top at one corner. The plan is a 4 by 3 rectangle with a 1 by 1 square drawn inside it at the corner where the cube sits — the square is a change of level, not a hole. The front elevation, looking along the 3 cm depth, is a 4 by 2 rectangle with a 1 by 1 square stepped up at one end, so the outline is a staircase. The side elevation, looking along the 4 cm width, is a 3 by 2 rectangle with the same 1 cm step. Three views, one scale, and each line drawn only where the surface actually changes.